A233129 -id:A233129 - cp's OEIS frontend

A233123 Number of n X 2 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

1, 8, 80, 896, 10496, 124928, 1495040, 17924096, 215023616, 2580021248, 30959206400, 371506282496, 4458058612736, 53496636243968, 641959366492160, 7703511324164096, 92442131595001856, 1109305561960153088

Offset: 1

R. H. Hardin, Dec 04 2013

nonn

Column 2 of A233129.

			Some solutions for n=5:
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..1..0....2..5....4..0....4..0....2..0....2..5....4..0....4..0....1..0....1..0
..0..1....0..4....5..2....2..1....0..2....4..3....2..1....5..2....5..2....5..1
..1..5....3..0....3..1....1..3....3..5....5..1....4..5....3..5....3..4....1..2
..0..4....0..2....0..2....2..4....0..4....1..3....0..1....0..2....1..0....0..1

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

A233129.

Empirical: a(n) = 16*a(n-1) - 48*a(n-2).
Conjectures from Colin Barker, Mar 19 2018: (Start)
G.f.: x*(1 - 8*x) / ((1 - 4*x)*(1 - 12*x)).
a(n) = 2^(2*n-3) * (3^n+3) / 3.
(End)

A233124 Number of n X 3 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

3, 80, 2688, 96256, 3497984, 127533056, 4653056000, 169793814528, 6196127858688, 226111237652480, 8251342992703488, 301111464108752896, 10988286523845115904, 400989192448372637696, 14633067014086637649920

Offset: 1

R. H. Hardin, Dec 04 2013

nonn

Column 3 of A233129.

			Some solutions for n=4:
..0..1..0....0..1..5....0..1..5....0..1..2....0..1..2....0..1..5....0..1..2
..2..5..2....2..0..4....4..5..2....1..2..1....4..3..5....2..5..2....3..0..1
..0..1..5....5..2..5....0..3..4....3..0..3....2..0..2....0..4..0....1..3..0
..3..5..4....1..5..4....3..1..2....0..3..5....0..3..5....1..0..1....3..4..2

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

Cf. A233129.

Empirical: a(n) = 48*a(n-1) - 448*a(n-2) + 1024*a(n-3).
Conjectures from Colin Barker, Mar 19 2018: (Start)
G.f.: x*(3 - 64*x + 192*x^2) / ((1 - 8*x)*(1 - 40*x + 128*x^2)).
a(n) = 8^(-1+n) + ((20-4*sqrt(17))^n*(-3+sqrt(17)) + (3+sqrt(17))*(4*(5+sqrt(17)))^n) / (32*sqrt(17)).
(End)

A233122 Number of n X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

1, 8, 2688, 10674176, 406142844928, 145451790488305664, 491056502853059022422016, 15650767090419537715133256040448, 4713550152014576979763161453081103695872

Offset: 1

R. H. Hardin, Dec 04 2013

nonn

Diagonal of A233129

			Some solutions for n=3
..0..1..0....0..1..2....0..1..0....0..1..2....0..1..2....0..1..2....0..1..2
..1..5..1....2..5..4....1..5..2....4..2..4....1..2..1....3..0..1....4..3..0
..2..1..2....5..2..5....2..1..0....5..1..0....3..0..2....0..1..5....5..1..3

R. H. Hardin, Table of n, a(n) for n = 1..13

A233125 Number of nX4 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabeled 6-colorings with no clashing color pairs).

Original entry on oeis.org

10, 896, 96256, 10674176, 1189609472, 132682612736, 14800557965312, 1651015493353472, 184172904936636416, 20544737466392772608, 2291793599167553601536, 255652719756086620454912

Offset: 1

R. H. Hardin, Dec 04 2013

nonn

Column 4 of A233129

			Some solutions for n=3
..0..1..0..2....0..1..2..4....0..1..0..2....0..1..5..4....0..1..0..2
..2..0..2..5....1..2..1..3....1..0..2..4....2..0..1..3....2..0..2..4
..5..2..1..2....3..4..5..1....5..3..4..5....5..1..3..1....1..2..4..0

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

Empirical: a(n) = 160*a(n-1) -6144*a(n-2) +86016*a(n-3) -393216*a(n-4).

Empirical: G.f.: -2*x*(-5+352*x-7168*x^2+40960*x^3) / ( (16*x-1)*(24576*x^3-3840*x^2+144*x-1) ). - R. J. Mathar, Oct 31 2015

A233126 Number of nX5 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

36, 10496, 3497984, 1189609472, 406142844928, 138791062863872, 47441169369530368, 16217390240149536768, 5543904365985920974848, 1895191786824003443752960, 647875237241500909514522624

Offset: 1

R. H. Hardin, Dec 04 2013

nonn

Column 5 of A233129

			Some solutions for n=2
..0..1..0..2..5....0..1..0..2..5....0..1..0..2..0....0..1..2..1..2
..1..0..4..5..2....1..0..2..5..2....2..5..1..0..1....4..2..4..3..4

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

Empirical: a(n) = 544*a(n-1) -82944*a(n-2) +5144576*a(n-3) -146800640*a(n-4) +1879048192*a(n-5) -8589934592*a(n-6)

A233127 Number of nX6 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

136, 124928, 127533056, 132682612736, 138791062863872, 145451790488305664, 152534173898504142848, 160000135886807521820672, 167846256915736431983329280, 176082743571854371127073701888

Offset: 1

R. H. Hardin, Dec 04 2013

nonn

Column 6 of A233129

			Some solutions for n=2
..0..1..2..4..2..0....0..1..2..5..1..5....0..1..0..1..5..2....0..1..0..4..2..1
..1..5..4..2..0..4....4..2..4..3..5..2....3..5..4..0..4..5....1..5..4..2..4..2

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

Empirical: a(n) = 1984*a(n-1) -1314816*a(n-2) +411303936*a(n-3) -70111985664*a(n-4) +6893422510080*a(n-5) -389708152569856*a(n-6) +11733988091625472*a(n-7) -145241087982698496*a(n-8)

A233128 Number of nX7 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

528, 1495040, 4653056000, 14800557965312, 47441169369530368, 152534173898504142848, 491056502853059022422016, 1581710916068322391195910144, 5095889238903796606027591319552

Offset: 1

R. H. Hardin, Dec 04 2013

nonn

Column 7 of A233129

			Some solutions for n=1
..0..1..0..4..5..4..5....0..1..0..4..5..1..5....0..1..0..2..0..4..2

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

Empirical: a(n) = 7168*a(n-1) -19070976*a(n-2) +26086473728*a(n-3) -21081846972416*a(n-4) +10809917287956480*a(n-5) -3649692508960587776*a(n-6) +824336623994081902592*a(n-7) -124561639357723747287040*a(n-8) +12414326720213201465638912*a(n-9) -792885332473813431379558400*a(n-10) +31062140009178282014900486144*a(n-11) -704387882353381376417601683456*a(n-12) +8398185226512019784915658735616*a(n-13) -40564819207303340847894502572032*a(n-14)

cp's OEIS Frontend

A233123 Number of n X 2 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

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A233124 Number of n X 3 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

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A233122 Number of n X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

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A233125 Number of nX4 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabeled 6-colorings with no clashing color pairs).

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A233126 Number of nX5 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

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A233127 Number of nX6 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

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A233128 Number of nX7 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

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