A238557 -id:A238557

A238556

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

+10
21

1, 3, 2, 1, 3, 4, 1, 6, 9, 1, 6, 21, 13, 4, 1, 9, 39, 53, 23, 1, 9, 64, 128, 87, 1, 12, 95, 283, 311, 91, 10, 1, 12, 133, 521, 891, 543, 106, 1, 15, 177, 917, 2118, 2030, 646, 1, 15, 228, 1444, 4424, 6000, 3295, 456, 25, 1, 18, 285, 2207, 8408, 15484, 13106, 4322, 473

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

OFFSET

3,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 3..971

Christopher Hunt Gribble, C++ program

EXAMPLE

The first 5 rows of T(n,k) are:

./ k 0 1 2 3 4 5 6

n

3 1 3 2

4 1 3 4

5 1 6 9

6 1 6 21 13 4

7 1 9 39 53 23

8 1 9 64 128 87

9 1 12 95 283 311 91 10

10 1 12 133 521 891 543 106

11 1 15 177 917 2118 2030 646

PROG

(C++) See Gribble link.

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550-A238552, A228166, A238555, 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 27 2015

Terms a(48) and beyond by Andrew Howroyd, May 29 2017

STATUS

approved

A238559

Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 8 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=4, 0<=k<=2*floor(n/4), read by rows.

+10
21

1, 3, 1, 1, 3, 2, 1, 6, 4, 1, 6, 6, 1, 9, 17, 5, 1, 1, 9, 32, 18, 4, 1, 12, 56, 46, 13, 1, 12, 84, 90, 31, 1, 15, 121, 193, 98, 13, 1, 1, 15, 162, 360, 275, 66, 6, 1, 18, 212, 664, 672, 250, 31, 1, 18, 266, 1080, 1408, 672, 110, 1, 21, 329, 1711, 2797, 1772, 432, 23, 1

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

OFFSET

4,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 4..992

Christopher Hunt Gribble, C++ program

EXAMPLE

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

.\ k 0 1 2 3 4 5 6

n

4 1 3 1

5 1 3 2

6 1 6 4

7 1 6 6

8 1 9 17 5 1

9 1 9 32 18 4

10 1 12 56 46 13

11 1 12 84 90 31

12 1 15 121 193 98 13 1

13 1 15 162 360 275 66 6

14 1 18 212 664 672 250 31

PROG

(C++) See Gribble link.

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550-A238552, A228166, A238555, A238556, A228167, A238557, A238558, 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 27 2015

Terms a(31) and beyond from Andrew Howroyd, May 29 2017

STATUS

approved

A238581

Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 9 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=4*floor(n/2), read by rows.

+10
21

1, 4, 12, 10, 3, 1, 4, 24, 40, 22, 1, 8, 65, 230, 467, 476, 269, 70, 9, 1, 8, 109, 641, 2281, 4424, 4718, 2409, 473, 1, 12, 182, 1479, 7644, 24024, 47022, 56226, 41000, 17834, 4545, 625, 39, 1, 12, 258, 2762, 19347, 86536, 255552, 495547, 625705, 499314, 239254, 61732, 6533

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

OFFSET

2,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 2..991

Christopher Hunt Gribble, C++ program

EXAMPLE

The first 4 rows of T(n,k) are:

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

n

2 1 4 12 10 3

3 1 4 24 40 22

4 1 8 65 230 467 476 269 70 9

5 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, A231145, A231473, A231568, A232440, A228165, A238550-A238552, A228166, A238555, A238556, A228167, A238557-A238559, A228168, A238582, A238583, A228169, A238586, A238592.

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Mar 01 2014

EXTENSIONS

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

Terms a(43) and beyond from Andrew Howroyd, May 29 2017

STATUS

approved

A238583

Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 9 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=4, 0<=k<=2*floor(n/4), read by rows.

+10
21

1, 3, 2, 1, 3, 4, 1, 6, 9, 1, 6, 14, 1, 9, 32, 18, 4, 1, 9, 55, 65, 23, 1, 12, 91, 164, 87, 1, 12, 132, 320, 229, 1, 15, 186, 608, 648, 134, 10, 1, 15, 245, 1043, 1633, 770, 106, 1, 18, 317, 1736, 3659, 2800, 646, 1, 18, 394, 2666, 7247, 7572, 2510

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

OFFSET

4,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 4..992

Christopher Hunt Gribble, C++ program

EXAMPLE

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

.\ k 0 1 2 3 4

n

4 1 3 2

5 1 3 4

6 1 6 9

7 1 6 14

8 1 9 32 18 4

9 1 9 55 65 23

10 1 12 91 164 87

11 1 12 132 320 229

PROG

(C++) See program link.

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550-A238552, A228166, A238555, A238556, A228167, A238557-A238559, A228168, A238581, A238582, A228169, A238586, A238592

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Mar 01 2014

EXTENSIONS

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

Terms a(26) and beyond from Andrew Howroyd, May 29 2017

STATUS

approved

A238586

Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 10 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=5*floor(n/2), read by rows.

+10
21

1, 5, 16, 19, 9, 1, 1, 5, 32, 73, 66, 10, 1, 10, 85, 377, 961, 1348, 1080, 472, 111, 12, 1, 1, 10, 142, 1011, 4429, 11370, 17252, 14478, 6094, 1020, 70, 1, 15, 236, 2280, 14203, 56571, 146212, 244063, 261847, 179063, 77974, 21422, 3637, 368, 24, 1

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

OFFSET

2,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 2..937

Christopher Hunt Gribble, C++ program

EXAMPLE

The first 4 rows of T(n,k) are:

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

n

2 1 5 16 19 9 1

3 1 5 32 73 66 10

4 1 10 85 377 961 1348 1080 472 111 12 1

5 1 10 142 1011 4429 11370 17252 14478 6094 1020 70

PROG

(C++) See Gribble link.

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550-A238552, A228166, A238555, A238556, A228167, A238557-A238559, A228168, A238581-A238583, A228169, A238592.

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Mar 01 2014

EXTENSIONS

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

Terms a(36) and beyond from Andrew Howroyd, May 29 2017

STATUS

approved

A238592

Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 10 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=3*floor(n/3), read by rows.

+10
21

1, 4, 9, 2, 1, 4, 18, 8, 1, 8, 42, 28, 1, 8, 77, 165, 151, 44, 6, 1, 12, 133, 521, 891, 543, 106, 1, 12, 200, 1160, 3022, 2756, 824, 1, 16, 288, 2260, 8443, 13336, 9364, 2819, 387, 20, 1, 16, 387, 3867, 19833, 48418, 58731, 34797, 9462, 900

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

OFFSET

3,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 3..989

Christopher Hunt Gribble, C++ program

EXAMPLE

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

.\ k 0 1 2 3 4 5 6

n

3 1 4 9 2

4 1 4 18 8

5 1 8 42 28

6 1 8 77 165 151 44 6

7 1 12 133 521 891 543 106

8 1 12 200 1160 3022 2756 824

PROG

(C++) See Gribble link.

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550-A238552, A228166, A238555, A238556, A228167, A238557-A238559, A228168, A238581-A238583, A228169, A238586.

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Mar 01 2014

EXTENSIONS

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

Terms a(36) and beyond from Andrew Howroyd, May 29 2017

STATUS

approved

A238558

Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 8 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=2*floor(n/3), read by rows.

+10
12

1, 3, 4, 1, 3, 8, 1, 6, 18, 1, 6, 36, 32, 13, 1, 9, 64, 128, 87, 1, 9, 100, 308, 332, 1, 12, 146, 647, 1118, 451, 68, 1, 12, 200, 1160, 3022, 2756, 824, 1, 15, 264, 1958, 6882, 10076, 5009, 1, 15, 336, 3020, 13798, 28774, 24237, 4774, 346

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

OFFSET

3,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 3..971

Christopher Hunt Gribble, C++ program

EXAMPLE

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

.\ k 0 1 2 3 4 5 6

n

3 1 3 4

4 1 3 8

5 1 6 18

6 1 6 36 32 13

7 1 9 64 128 87

8 1 9 100 308 332

9 1 12 146 647 1118 451 68

10 1 12 200 1160 3022 2756 824

PROG

(C++) See Gribble link.

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, 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 28 2014

EXTENSIONS

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

Terms a(41) and beyond from Andrew Howroyd, May 29 2017

STATUS

approved

A238582

Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 9 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=2*floor(n/3), read by rows.

+10
12

1, 4, 6, 1, 1, 4, 12, 3, 1, 8, 28, 10, 1, 8, 54, 82, 49, 8, 1, 1, 12, 95, 283, 311, 91, 10, 1, 12, 146, 647, 1118, 451, 68, 1, 16, 212, 1300, 3380, 3076, 1200, 209, 20, 1, 1, 16, 288, 2260, 8443, 13336, 9364, 2819, 387, 20

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

OFFSET

3,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 3..989

Christopher Hunt Gribble, C++ program

EXAMPLE

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

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

n

3 1 4 6 1

4 1 4 12 3

5 1 8 28 10

6 1 8 54 82 49 8 1

7 1 12 95 283 311 91 10

8 1 12 146 647 1118 451 68

9 1 16 212 1300 3380 3076 1200 209 20 1

10 1 16 288 2260 8443 13336 9364 2819 387 20

11 1 20 379 3709 18203 42412 44599 19051 3682 282

PROG

(C++) See Gribble link.

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550-A238552, A228166, A238555, A238556, A228167, A238557-A238559, A228168, A238581, A238583, A228169, A238586, A238592.

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Mar 01 2014

EXTENSIONS

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

Terms a(46) and beyond from Andrew Howroyd, May 29 2017

STATUS

approved

A238551

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

+10
10

1, 2, 1, 1, 2, 2, 1, 4, 4, 1, 4, 11, 3, 1, 1, 6, 21, 13, 4, 1, 6, 36, 32, 13, 1, 8, 54, 82, 49, 8, 1, 1, 8, 77, 165, 151, 44, 6, 1, 10, 103, 319, 382, 173, 31, 1, 10, 134, 530, 867, 559, 164, 12, 1, 1, 12, 168, 852, 1789, 1632, 705, 119, 9

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

OFFSET

3,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 3..971

Christopher Hunt Gribble, C++ program

EXAMPLE

The first 12 rows of T(n,k) are:

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

n

3 1 2 1

4 1 2 2

5 1 4 4

6 1 4 11 3 1

7 1 6 21 13 4

8 1 6 36 32 13

9 1 8 54 82 49 8 1

10 1 8 77 165 151 44 6

11 1 10 103 319 382 173 31

12 1 10 134 530 867 559 164 12 1

13 1 12 168 852 1789 1632 705 119 9

14 1 12 207 1255 3409 4074 2406 618 66

PROG

(C++) See Gribble link.

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550, A238552, 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(57) and beyond from Andrew Howroyd, May 29 2017

STATUS

approved

A257523

Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 7 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=4, 0<=k<=floor(n/4), read by rows.

+10
1

1, 2, 1, 2, 1, 4, 1, 4, 1, 6, 6, 1, 6, 14, 1, 8, 28, 1, 8, 44, 1, 10, 66, 20, 1, 10, 90, 64, 1, 12, 120, 168, 1, 12, 152, 320, 1, 14, 190, 572, 72, 1, 14, 230, 896, 328, 1, 16, 276, 1360, 984, 1, 16, 324, 1920, 2264, 1, 18, 378, 2660, 4528, 272

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

OFFSET

4,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 4..860

Christopher Hunt Gribble, C++ program

EXAMPLE

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

.\ k 0 1 2 3

n

4 1 2

5 1 2

6 1 4

7 1 4

8 1 6 6

9 1 6 14

10 1 8 28

11 1 8 44

12 1 10 66 20

13 1 10 90 64

14 1 12 120 168

15 1 12 152 320

PROG

(PARI)

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

for(n=4, 15, for(k=0, (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, A238552, A228166, A238555, A238556, A228167, A238557, A238558, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Apr 27 2015

EXTENSIONS

Terms a(24) and beyond by Andrew Howroyd, May 29 2017

STATUS

approved