A214187 -id:A214187

A214188

Number of 0..6 colorings of a 1 X (n+1) array circular in the n+1 direction with new values 0..6 introduced in row major order.

+10
2

1, 1, 4, 11, 41, 162, 714, 3397, 17251, 92048, 509444, 2893683, 16734381, 97965934, 578241694, 3431848769, 20442513431, 122066210220, 730058053464, 4371040179055, 26189154314401, 156987015743306, 941331763528754

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

OFFSET

1,3

COMMENTS

Row 1 of A214187.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 15*a(n-1) - 79*a(n-2) + 165*a(n-3) - 64*a(n-4) - 180*a(n-5) + 144*a(n-6).

Empirical g.f.: x*(1 - 14*x + 68*x^2 - 135*x^3 + 91*x^4) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 6*x)). - Colin Barker, Mar 09 2018

EXAMPLE

Some solutions for n=4:

..0..1..2..0..3.....0..1..2..0..1.....0..1..0..1..2.....0..1..2..1..2

CROSSREFS

Cf. A214187.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 07 2012

STATUS

approved

A214181

Number of 0..6 colorings of an n X 3 array circular in the 3 direction with new values 0..6 introduced in row major order.

+10
1

1, 18, 1046, 108893, 13701111, 1808609113, 241491378451, 32332391658753, 4331663509964171, 580414863999963833, 77774694477831007731, 10421780348518296089713, 1396517647955429913843931

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

OFFSET

1,2

COMMENTS

Column 2 of A214187.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 179*a(n-1) - 6468*a(n-2) + 59396*a(n-3) - 94336*a(n-4).

Conjectures from Colin Barker, Jul 22 2018: (Start)

G.f.: x*(1 - 161*x + 4292*x^2 - 21313*x^3) / ((1 - 2*x)*(1 - 11*x)*(1 - 32*x)*(1 - 134*x)).

a(n) = (2^(n-4)*(67^(n-1)+9) + 11^(n-1) + 3*2^(5*n-7))/3.

(End)

EXAMPLE

Some solutions for n=4:

..0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2

..1..0..3....1..0..3....3..0..1....1..2..3....1..2..3....1..2..3....1..0..3

..3..4..1....0..3..1....0..1..2....3..0..1....0..1..4....0..1..4....3..4..0

..4..0..2....1..4..0....1..0..3....4..1..5....4..2..0....1..0..5....0..5..1

CROSSREFS

Cf. A214187.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 07 2012

STATUS

approved

A214182

Number of 0..6 colorings of an nX4 array circular in the 4 direction with new values 0..6 introduced in row major order

+10
1

4, 353, 147943, 96673866, 68272896836, 48807260151073, 34958661918205401, 25047104071770605888, 17946563397124532921734, 12859036484490635332784967, 9213742993368664938803040203, 6601822515414603719492440676662

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

OFFSET

1,1

COMMENTS

Column 3 of A214187

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 902*a(n-1) -142783*a(n-2) +7297504*a(n-3) -157308287*a(n-4) +1529846974*a(n-5) -7002462289*a(n-6) +14489273756*a(n-7) -12535263856*a(n-8) +3668758080*a(n-9)

EXAMPLE

Some solutions for n=4

..0..1..2..3....0..1..0..1....0..1..2..1....0..1..2..1....0..1..0..1

..1..3..1..4....1..0..1..2....1..0..3..4....2..3..4..5....1..0..2..0

..3..1..0..5....0..1..0..1....0..1..2..5....1..2..3..4....2..1..3..1

..5..2..3..4....3..4..5..4....6..0..1..4....5..4..0..6....4..2..1..2

KEYWORD

nonn

AUTHOR

R. H. Hardin Jul 07 2012

STATUS

approved

A214183

Number of 0..6 colorings of an nX5 array circular in the 5 direction with new values 0..6 introduced in row major order

+10
1

11, 7434, 21418431, 76892349394, 282135060192286, 1037404464993610934, 3815299253956873853106, 14031944174294607018138494, 51606920496933612048613391186, 189800837547185166387283413516334

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

OFFSET

1,1

COMMENTS

Column 4 of A214187

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..106

FORMULA

Empirical: a(n) = 4178*a(n-1) -1895863*a(n-2) +209149752*a(n-3) -7928550662*a(n-4) +84119844576*a(n-5) -298704239064*a(n-6) +219967475904*a(n-7)

EXAMPLE

Some solutions for n=4

..0..1..0..1..2....0..1..0..1..2....0..1..2..0..1....0..1..2..0..1

..1..3..4..5..4....1..2..1..0..3....1..0..1..2..3....1..3..4..1..4

..5..1..0..1..6....0..1..2..1..2....0..1..2..1..2....0..1..0..2..1

..2..4..1..4..1....1..2..3..2..3....3..4..0..5..4....1..2..3..0..2

KEYWORD

nonn

AUTHOR

R. H. Hardin Jul 07 2012

STATUS

approved

A214184

Number of 0..6 colorings of an n X 6 array circular in the 6 direction with new values 0..6 introduced in row major order.

+10
1

41, 198052, 3375824210, 63801460335656, 1213459476427300800, 23088156449777055684502, 439302572451496835864263417, 8358702906469803762741273286892, 159042821944647153392175946109898897

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

OFFSET

1,1

COMMENTS

Column 5 of A214187.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..35

EXAMPLE

Some solutions for n=4

..0..1..0..1..0..1....0..1..2..0..1..2....0..1..2..0..1..2....0..1..0..1..0..1

..1..0..1..0..1..0....1..0..3..1..0..3....2..0..1..2..3..4....1..0..1..0..1..0

..0..1..0..1..0..1....0..2..4..5..3..1....0..1..2..4..2..3....0..1..0..1..2..3

..1..0..1..0..1..0....6..0..5..4..0..5....3..5..0..3..1..5....1..4..5..6..3..4

CROSSREFS

Cf. A214187.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 07 2012

STATUS

approved

A214185

Number of 0..6 colorings of an nX7 array circular in the 7 direction with new values 0..6 introduced in row major order

+10
1

162, 5731144, 537471327779, 52728429977071820, 5181849398711430701208, 509276783285147027391376400, 50052307567860864303157948860474, 4919198813277559761012684429315089098

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

OFFSET

1,1

COMMENTS

Column 6 of A214187

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..12

EXAMPLE

Some solutions for n=4

..0..1..2..0..1..0..2....0..1..0..1..0..1..2....0..1..2..0..1..0..2

..1..0..1..2..0..1..0....1..2..1..0..1..2..3....1..0..1..2..3..1..3

..2..1..2..3..4..5..1....3..4..5..4..0..4..1....2..4..3..1..0..5..6

..3..2..5..6..3..4..5....1..3..6..1..2..6..0....1..3..4..6..1..4..0

KEYWORD

nonn

AUTHOR

R. H. Hardin Jul 07 2012

STATUS

approved

A214189

Number of 0..6 colorings of a 2X(n+1) array circular in the n+1 direction with new values 0..6 introduced in row major order

+10
1

4, 18, 353, 7434, 198052, 5731144, 172707247, 5290686318, 163203090770, 5048858758020, 156379568912461, 4846014558069802, 150203703987575008, 4656019290676790496, 144332757507860933195, 4474265565293272517286

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

OFFSET

1,1

COMMENTS

Row 2 of A214187

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 39*a(n-1) -133*a(n-2) -3905*a(n-3) +6437*a(n-4) +125497*a(n-5) +83961*a(n-6) -931595*a(n-7) -1308936*a(n-8) +809964*a(n-9) +1218672*a(n-10)

EXAMPLE

Some solutions for n=4

..0..1..2..3..1....0..1..0..1..2....0..1..2..0..1....0..1..2..0..1

..2..3..0..1..0....2..3..1..0..1....3..4..5..3..6....1..2..0..1..0

KEYWORD

nonn

AUTHOR

R. H. Hardin Jul 07 2012

STATUS

approved

A214190

Number of 0..6 colorings of a 3X(n+1) array circular in the n+1 direction with new values 0..6 introduced in row major order

+10
1

34, 1046, 147943, 21418431, 3375824210, 537471327779, 85978533129243, 13765597336821245, 2204602881329983688, 353096564867070887951, 56554251279074204230121, 9058140154145997330337181

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

OFFSET

1,1

COMMENTS

Row 3 of A214187

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 139*a(n-1) +5515*a(n-2) -286157*a(n-3) -9529273*a(n-4) +113179647*a(n-5) +4029123791*a(n-6) -21482035001*a(n-7) -665136918315*a(n-8) +3470737828565*a(n-9) +52035528093885*a(n-10) -353663596245035*a(n-11) -1772488823978235*a(n-12) +18597082646494445*a(n-13) +6436724051209165*a(n-14) -461676350902794315*a(n-15) +989689896962549920*a(n-16) +4490761773386882420*a(n-17) -20885571816583158340*a(n-18) +2406786493445125820*a(n-19) +135386533520490778816*a(n-20) -242458279252260285504*a(n-21) -117064394722434074400*a(n-22) +741048574341017155392*a(n-23) -533060382247946111232*a(n-24) -464734745166440627712*a(n-25) +719025841858074960384*a(n-26) -101164868845572040704*a(n-27) -184396432098202951680*a(n-28) +60855200138907648000*a(n-29)

EXAMPLE

Some solutions for n=4

..0..1..0..1..2....0..1..0..1..2....0..1..2..1..2....0..1..0..1..2

..3..0..1..2..0....1..2..3..0..3....1..0..1..3..4....1..2..1..0..3

..0..4..5..1..2....3..0..1..2..0....4..1..2..0..5....2..3..4..3..5

KEYWORD

nonn

AUTHOR

R. H. Hardin Jul 07 2012

STATUS

approved

A214191

Number of 0..6 colorings of a 4X(n+1) array circular in the n+1 direction with new values 0..6 introduced in row major order

+10
1

499, 108893, 96673866, 76892349394, 63801460335656, 52728429977071820, 43640411285319502254, 36112297704840189696506, 29884457546802474331953680, 24730452099783783516454127661, 20465374817193973734647830403223

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

OFFSET

1,1

COMMENTS

Row 4 of A214187

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..148

EXAMPLE

Some solutions for n=4

..0..1..2..3..1....0..1..0..1..2....0..1..0..1..2....0..1..2..0..1

..2..3..0..1..0....1..2..1..2..3....1..2..1..0..3....3..4..5..3..6

..0..4..5..6..3....0..3..0..1..2....0..1..2..1..2....4..1..6..5..2

..6..5..0..4..5....1..0..1..0..3....1..2..3..2..3....6..2..1..4..5

KEYWORD

nonn

AUTHOR

R. H. Hardin Jul 07 2012

STATUS

approved

A214192

Number of 0..6 colorings of a 5X(n+1) array circular in the n+1 direction with new values 0..6 introduced in row major order

+10
1

10507, 13701111, 68272896836, 282135060192286, 1213459476427300800, 5181849398711430701208, 22161121532525857186165916, 94747979794440013487452463352, 405111926950578638476251757606722

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

OFFSET

1,1

COMMENTS

Row 5 of A214187

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..24

EXAMPLE

Some solutions for n=4

..0..1..2..0..1....0..1..0..1..2....0..1..2..0..1....0..1..2..0..1

..1..2..0..1..0....2..3..2..3..0....2..0..1..2..0....1..0..1..3..2

..2..0..1..0..1....0..1..4..2..4....1..2..3..0..2....2..1..0..1..3

..0..2..3..4..5....1..0..5..3..5....0..3..4..5..1....0..3..4..5..4

..1..3..1..5..6....2..1..6..2..3....6..0..3..4..3....5..1..0..1..6

KEYWORD

nonn

AUTHOR

R. H. Hardin Jul 07 2012

STATUS

approved