A238557 -id:A238557

A238009

Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 3 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=floor(n/2), read by rows.

+10
23

1, 1, 1, 1, 1, 2, 2, 1, 2, 4, 1, 3, 8, 3, 1, 3, 12, 8, 1, 4, 18, 22, 6, 1, 4, 24, 40, 22, 1, 5, 32, 73, 66, 10, 1, 5, 40, 112, 146, 48, 1, 6, 50, 172, 292, 174, 20, 1, 6, 60, 240, 516, 448, 116, 1, 7, 72, 335, 860, 1020, 464, 36, 1, 7, 84, 440, 1340, 2016, 1360, 256

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,6

LINKS

Christopher Hunt Gribble and Andrew Howroyd, Rows n=2..60 of T(n,k) flattened (Rows n=2..20 from Christopher Hunt Gribble)

Christopher Hunt Gribble, C++ program

EXAMPLE

The first 19 rows of T(n,k) are:

n\k 0 1 2 3 4 5 6 7 8 9 10

2 1 1

3 1 1

4 1 2 2

5 1 2 4

6 1 3 8 3

7 1 3 12 8

8 1 4 18 22 6

9 1 4 24 40 22

10 1 5 32 73 66 10

11 1 5 40 112 146 48

12 1 6 50 172 292 174 20

13 1 6 60 240 516 448 116

14 1 7 72 335 860 1020 464 36

15 1 7 84 440 1340 2016 1360 256

16 1 8 98 578 2010 3716 3400 1168 72

17 1 8 112 728 2890 6336 7432 3840 584

18 1 9 128 917 4046 10326 14864 10600 2920 136

19 1 9 144 1120 5502 16016 27536 25344 10600 1280

20 1 10 162 1368 7336 24066 48188 54992 31800 7080 272

PROG

(C++) See Gribble link.

(PARI)

T(n, k)={(2^k*binomial(n-1*k, k) + ((k%2==0)+(n%2==0||k%2==0)+(k==0)) * 2^((k+1)\2)*binomial((n-1*k-(k%2)-(n%2))/2, k\2))/4}

for(n=2, 20, for(k=0, floor(n/2), print1(T(n, k), ", ")); print) \\ Andrew Howroyd, May 29 2017

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550, A238551, A238552, A228166, A238555, A238556, A228167, A238557, A238558, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592.

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Feb 16 2014

EXTENSIONS

Corrected C++ program and xrefs added by Christopher Hunt Gribble, Apr 25 2015

STATUS

approved

A231145

Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 5 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=n-n%2, read by rows.

+10
22

1, 2, 2, 1, 2, 4, 1, 4, 13, 10, 4, 1, 4, 23, 35, 23, 1, 6, 40, 101, 125, 54, 10, 1, 6, 58, 206, 403, 336, 106, 1, 8, 83, 392, 1056, 1438, 956, 240, 25, 1, 8, 109, 641, 2281, 4424, 4718, 2409, 473, 1, 10, 142, 1011, 4429, 11370, 17252, 14478, 6094, 1020, 70

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 2..967 (terms n=2..71 from Christopher Hunt Gribble)

Christopher Hunt Gribble, C++ program

EXAMPLE

The first 8 rows of T(n,k) are:

.\ k 0 1 2 3 4 5 6 7 8

n

2 1 2 2

3 1 2 4

4 1 4 13 10 4

5 1 4 23 35 23

6 1 6 40 101 125 54 10

7 1 6 58 206 403 336 106

8 1 8 83 392 1056 1438 956 240 25

9 1 8 109 641 2281 4424 4718 2409 473

PROG

(C++) See Gribble link.

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231473, A231568, A232440, A228165, A238550, A238551, A238552, A228166, A238555, A238556, A228167, A238557, A238558, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592.

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Feb 23 2014

EXTENSIONS

Terms corrected and xrefs updated by Christopher Hunt Gribble, Apr 26 2015

STATUS

approved

A231473

Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 5 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=floor(n/3), read by rows.

+10
21

1, 2, 1, 2, 1, 4, 1, 4, 4, 1, 6, 9, 1, 6, 18, 1, 8, 28, 10, 1, 8, 42, 28, 1, 10, 57, 76, 1, 10, 76, 140, 25, 1, 12, 96, 254, 107, 1, 12, 120, 392, 321, 1, 14, 145, 600, 731, 70, 1, 14, 174, 840, 1462, 366, 1, 16, 204, 1170, 2610, 1308, 1, 16, 238, 1540, 4350, 3416, 196

(list; graph; refs; listen; history; text; internal format)

OFFSET

3,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 3..974

Christopher Hunt Gribble, C++ program

EXAMPLE

The first 11 rows of T(n,k) are:

.\ k 0 1 2 3 4

n

3 1 2

4 1 2

5 1 4

6 1 4 4

7 1 6 9

8 1 6 18

9 1 8 28 10

10 1 8 42 28

11 1 10 57 76

12 1 10 76 140 25

13 1 12 96 254 107

MATHEMATICA

T[n_, k_] := ((3^k + 1)*Binomial[n - 2k, k] + Boole[EvenQ[k] || OddQ[n]]*(3^(Quotient[(k + 1), 2]) + 3^Quotient[k, 2]) Binomial[(n - 2k - Mod[n, 2])/2, Quotient[k, 2]])/4; Table[T[n, k], {n, 3, 20}, {k, 0, Floor[n/3]}] // Flatten (* Jean-François Alcover, Oct 06 2017, after Andrew Howroyd *)

PROG

(C++) See Gribble link.

(PARI)

T(n, k)={((3^k+1)*binomial(n-2*k, k) + (k%2==0||n%2==1) * (3^((k+1)\2)+3^(k\2)) * binomial((n-2*k-(n%2))/2, k\2))/4}

for(n=3, 20, for(k=0, floor(n/3), print1(T(n, k), ", ")); print) \\ Andrew Howroyd, May 29 2017

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231568, A232440, A228165, A238550-A238552, A228166, A238555, A238556, A228167, A238557-A238559, A228168, A238581-A238583, A228169, A238586, A238592.

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Feb 23 2014

EXTENSIONS

Terms corrected and xrefs updated by Christopher Hunt Gribble, Apr 26 2015

Terms a(40) and beyond from Andrew Howroyd, May 29 2017

STATUS

approved

A231568

Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 5 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=4, 0<=k<=floor(n/4), read by rows.

+10
21

1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 1, 3, 4, 1, 4, 8, 1, 4, 12, 1, 5, 18, 3, 1, 5, 24, 8, 1, 6, 32, 22, 1, 6, 40, 40, 1, 7, 50, 73, 6, 1, 7, 60, 112, 22, 1, 8, 72, 172, 66, 1, 8, 84, 240, 146, 1, 9, 98, 335, 292, 10, 1, 9, 112, 440, 516, 48, 1, 10, 128, 578, 860, 174

(list; graph; refs; listen; history; text; internal format)

OFFSET

4,6

LINKS

Andrew Howroyd, Table of n, a(n) for n = 4..989

Christopher Hunt Gribble, C++ program

EXAMPLE

The first 14 rows of T(n,k) are:

.\ k 0 1 2 3 4

n

4 1 1

5 1 1

6 1 2

7 1 2

8 1 3 2

9 1 3 4

10 1 4 8

11 1 4 12

12 1 5 18 3

13 1 5 24 8

14 1 6 32 22

15 1 6 40 40

16 1 7 50 73 6

17 1 7 60 112 22

MATHEMATICA

T[n_, k_] := (2^k Binomial[n - 3k, k] + (Boole[EvenQ[k]] + Boole[EvenQ[n] || EvenQ[k]] + Boole[k == 0]) 2^Quotient[k+1, 2] Binomial[(n - 3k - Mod[k, 2] - Mod[n, 2])/2, Quotient[k, 2]])/4; Table[T[n, k], {n, 4, 20}, {k, 0, Floor[n/4]}] // Flatten (* Jean-François Alcover, Oct 06 2017, after Andrew Howroyd *)

PROG

(C++) See Gribble link.

(PARI)

T(n, k)={(2^k*binomial(n-3*k, k) + ((k%2==0)+(n%2==0||k%2==0)+(k==0)) * 2^((k+1)\2)*binomial((n-3*k-(k%2)-(n%2))/2, k\2))/4}

for(n=2, 20, for(k=0, floor(n/4), print1(T(n, k), ", ")); print) \\ Andrew Howroyd, May 29 2017

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A232440, A228165, A238550, A238551, A238552, A228166, A238555, A238556, A228167, A238557, A238558, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592.

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Feb 23 2014

EXTENSIONS

Terms extended and xrefs updated by Christopher Hunt Gribble, Apr 26 2015

Terms a(32) and beyond from Andrew Howroyd, May 29 2017

STATUS

approved

A232440

Number T(n,k) of equivalence classes of ways of placing k 5 X 5 tiles in an n X 5 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=5, 0<=k<=floor(n/5), read by rows.

+10
21

1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 3, 1, 1, 4, 2, 1, 4, 4, 1, 5, 6, 1, 5, 9, 1, 6, 12, 1, 1, 6, 16, 2, 1, 7, 20, 6, 1, 7, 25, 10, 1, 8, 30, 19, 1, 8, 36, 28, 1, 1, 9, 42, 44, 3, 1, 9, 49, 60, 9, 1, 10, 56, 85, 19, 1, 10, 64, 110, 38, 1, 11, 72, 146, 66, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

5,6

LINKS

Andrew Howroyd, Table of n, a(n) for n = 5..989

Christopher Hunt Gribble, C++ program

EXAMPLE

The first 9 rows of T(n,k) are:

.\ k 0 1 2

n

5 1 1

6 1 1

7 1 2

8 1 2

9 1 3

10 1 3 1

11 1 4 2

12 1 4 4

13 1 5 6

MATHEMATICA

T[n_, k_] := (Binomial[n - 4k, k] + Boole[EvenQ[k] || OddQ[n]] Binomial[(n - 4k - Mod[n, 2])/2, Quotient[k, 2]])/2; Table[T[n, k], {n, 5, 20}, {k, 0, Quotient[n, 5]}] // Flatten (* Jean-François Alcover, Oct 06 2017, after Andrew Howroyd *)

PROG

(C++) See Gribble link.

(PARI)

T(n, k)={(binomial(n-4*k, k) + (k%2==0||n%2==1)*binomial((n-4*k-n%2)/2, k\2))/2}

for(n=5, 20, for(k=0, (n\5), print1(T(n, k), ", ")); print) \\ Andrew Howroyd, May 29 2017

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A228165, A238550-A238552, A228166, A238555, A238556, A228167, A238557-A238559, A228168, A238581-A238583, A228169, A238586, A238592.

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Feb 23 2014

EXTENSIONS

Terms extended and xrefs updated by Christopher Hunt Gribble, Apr 26 2015

Terms a(27) and beyond from Andrew Howroyd, May 29 2017

STATUS

approved

A238189

Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 4 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=n-n%2, read by rows.

+10
21

1, 2, 1, 1, 2, 2, 1, 4, 7, 3, 1, 1, 4, 13, 10, 4, 1, 6, 23, 33, 22, 6, 1, 1, 6, 34, 68, 72, 30, 6, 1, 8, 49, 139, 204, 145, 54, 8, 1, 1, 8, 65, 230, 467, 476, 269, 70, 9, 1, 10, 85, 377, 961, 1348, 1080, 472, 111, 12, 1, 1, 10, 106, 552, 1767, 3188, 3454, 2156

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 2..967 (terms n=2..127 from Christopher Hunt Gribble)

Christopher Hunt Gribble, C++ program

EXAMPLE

The first 10 rows of T(n,k) are:

k 0 1 2 3 4 5 6 7 8 9 10

n

2 1 2 1

3 1 2 2

4 1 4 7 3 1

5 1 4 13 10 4

6 1 6 23 33 22 6 1

7 1 6 34 68 72 30 6

8 1 8 49 139 204 145 54 8 1

9 1 8 65 230 467 476 269 70 9

10 1 10 85 377 961 1348 1080 472 111 12 1

11 1 10 106 552 1767 3188 3454 2156 779 140 12

PROG

(C++) See Gribble link.

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550, A238551, A238552, A228166, A238555, A238556, A228167, A238557, A238558, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592.

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Feb 19 2014

EXTENSIONS

Terms corrected and extended by Christopher Hunt Gribble, Apr 25 2015

STATUS

approved

A238190

Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 4 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=floor(n/3), read by rows.

+10
21

1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 3, 4, 1, 3, 8, 1, 4, 12, 3, 1, 4, 18, 8, 1, 5, 24, 22, 1, 5, 32, 40, 6, 1, 6, 40, 73, 22, 1, 6, 50, 112, 66, 1, 7, 60, 172, 146, 10, 1, 7, 72, 240, 292, 48, 1, 8, 84, 335, 516, 174, 1, 8, 98, 440, 860, 448, 20

(list; graph; refs; listen; history; text; internal format)

OFFSET

3,6

LINKS

Andrew Howroyd, Table of n, a(n) for n = 3..974

Christopher Hunt Gribble, C++ program

EXAMPLE

The first 13 rows of T(n,k) are:

.\ k 0 1 2 3 4 5

n

3 1 1

4 1 1

5 1 2

6 1 2 2

7 1 3 4

8 1 3 8

9 1 4 12 3

10 1 4 18 8

11 1 5 24 22

12 1 5 32 40 6

13 1 6 40 73 22

14 1 6 50 112 66

15 1 7 60 172 146 10

MATHEMATICA

T[n_, k_] := (2^k Binomial[n - 2k, k] + (Boole[EvenQ[k]] + Boole[OddQ[n] || EvenQ[k]] + Boole[k == 0]) 2^Quotient[k + 1, 2] Binomial[(n - 2k - Mod[n, 2])/2, Quotient[k, 2]])/4; Table[T[n, k], {n, 3, 20}, {k, 0, Floor[n/3]}] // Flatten (* Jean-François Alcover, Oct 06 2017, after Andrew Howroyd *)

PROG

(C++) See Gribble link.

(PARI)

T(n, k)={(2^k*binomial(n-2*k, k) + ((k%2==0)+(n%2==1||k%2==0)+(k==0)) * 2^((k+1)\2)*binomial((n-2*k-(n%2))/2, k\2))/4}

for(n=2, 20, for(k=0, floor(n/3), print1(T(n, k), ", ")); print) \\ Andrew Howroyd, May 29 2017

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550, A238551, A238552, A228166, A238555, A238556, A228167, A238557, A238558, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592.

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Feb 19 2014

EXTENSIONS

Link to C++ program and xrefs updated by Christopher Hunt Gribble, Apr 25 2015

Terms a(51) and beyond from Andrew Howroyd, May 29 2017

STATUS

approved

A238550

Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 6 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=3*floor(n/2), read by rows.

+10
21

1, 3, 4, 1, 1, 3, 8, 3, 1, 6, 23, 33, 22, 6, 1, 1, 6, 40, 101, 125, 54, 10, 1, 9, 68, 262, 534, 532, 276, 74, 12, 1, 1, 9, 98, 509, 1551, 2505, 2196, 971, 219, 20, 1, 12, 139, 927, 3731, 8772, 12069, 9506, 4366, 1160, 179, 16, 1, 1, 12, 182, 1479, 7644, 24024

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 2..953 (terms n=2..69 from Christopher Hunt Gribble)

Christopher Hunt Gribble, C++ program

EXAMPLE

The first 6 rows of T(n,k) are:

.\ k 0 1 2 3 4 5 6 7 8 9

n

2 1 3 4 1

3 1 3 8 3

4 1 6 23 33 22 6 1

5 1 6 40 101 125 54 10

6 1 9 68 262 534 532 276 74 12 1

7 1 9 98 509 1551 2505 2196 971 219 20

PROG

(C++) See Gribble link.

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238551, A238552, A228166, A238555, A238556, A228167, A238557-A238559, A228168, A238581-A238583, A228169, A238586, A238592.

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Feb 28 2014

EXTENSIONS

Terms corrected and xrefs updated by Christopher Hunt Gribble, Apr 26 2015

STATUS

approved

A238552

Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 6 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=4, 0<=k<=floor(n/4), read by rows.

+10
21

1, 2, 1, 2, 1, 4, 1, 4, 1, 6, 4, 1, 6, 9, 1, 8, 18, 1, 8, 28, 1, 10, 42, 10, 1, 10, 57, 28, 1, 12, 76, 76, 1, 12, 96, 140, 1, 14, 120, 254, 25, 1, 14, 145, 392, 107, 1, 16, 174, 600, 321, 1, 16, 204, 840, 731, 1, 18, 238, 1170, 1462, 70, 1, 18, 273, 1540, 2610, 366

(list; graph; refs; listen; history; text; internal format)

OFFSET

4,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 4..989

Christopher Hunt Gribble, C++ program

EXAMPLE

The first 14 rows of T(n,k) are:

.\ k 0 1 2 3 4

n

4 1 2

5 1 2

6 1 4

7 1 4

8 1 6 4

9 1 6 9

10 1 8 18

11 1 8 28

12 1 10 42 10

13 1 10 57 28

14 1 12 76 76

15 1 12 96 140

16 1 14 120 254 25

17 1 14 145 392 107

MATHEMATICA

T[n_, k_] := ((3^k + 1) Binomial[n - 3k, k] + Boole[EvenQ[k] || EvenQ[n]]*(3^Quotient[k + 1, 2] + 3^Quotient[k, 2]) * Binomial[(n - 3k - Mod[k, 2] - Mod[n, 2])/2, Quotient[k, 2]])/4; Table[T[n, k], {n, 4, 20}, {k, 0, Floor[n/4]}] // Flatten (* Jean-François Alcover, Oct 06 2017, after Andrew Howroyd *)

PROG

(C++) See Gribble link.

(PARI)

T(n, k)={((3^k+1)*binomial(n-3*k, k) + (k%2==0||n%2==0) * (3^((k+1)\2)+3^(k\2)) * binomial((n-3*k-(k%2)-(n%2))/2, k\2))/4}

for(n=4, 20, for(k=0, floor(n/4), print1(T(n, k), ", ")); print) \\ Andrew Howroyd, May 29 2017

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550, A238551, A228166, A238555, A238556, A228167, A238557, A238558, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592.

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Feb 28 2014

EXTENSIONS

Terms corrected and xrefs updated by Christopher Hunt Gribble, Apr 27 2015

Terms a(28) and beyond from Andrew Howroyd, May 29 2017

STATUS

approved

A238555

Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 7 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=3*floor(n/2), read by rows.

+10
21

1, 3, 6, 2, 1, 3, 12, 8, 1, 6, 34, 68, 72, 30, 6, 1, 6, 58, 206, 403, 336, 106, 1, 9, 98, 509, 1551, 2505, 2196, 971, 219, 20, 1, 9, 140, 980, 4248, 10592, 15614, 12876, 5462, 900, 1, 12, 198, 1742, 9748, 33644, 73274, 98779, 80661, 37886, 9679, 1258, 72

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 2..953

Christopher Hunt Gribble, C++ program

EXAMPLE

The first 6 rows of T(n,k) are:

./ k 0 1 2 3 4 5 6 7 8 9

n

2 1 3 6 2

3 1 3 12 8

4 1 6 34 68 72 30 6

5 1 6 58 206 403 336 106

6 1 9 98 509 1551 2505 2196 971 219 20

7 1 9 140 980 4248 10592 15614 12876 5462 900

PROG

(C++) See Gribble link.

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550, A238551, A238552, A228166, A238556, A228167, A238557, A238558, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592.

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Feb 28 2014

EXTENSIONS

Terms corrected and xrefs updated by Christopher Hunt Gribble, Apr 27 2015

STATUS

approved