A232161 -id:A232161 - cp's OEIS frontend

A232155 Number of n X 2 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, vertically or antidiagonally, and no adjacent values equal.

2, 18, 62, 218, 746, 2600, 9004, 31262, 108492, 376566, 1307146, 4537292, 15750222, 54673186, 189786782, 658806476, 2286917482, 7938591212, 27557292770, 95659868830, 332064969492, 1152700237642, 4001379292082, 13890026339060

Offset: 1

R. H. Hardin, Nov 19 2013

nonn

			Some solutions for n=7:
..2..1....2..3....3..1....0..3....1..3....0..1....0..1....2..1....3..0....1..2
..3..0....0..1....0..2....1..2....2..1....2..3....3..2....3..2....1..3....0..3
..2..3....2..3....3..1....3..0....3..0....1..2....0..1....1..0....2..0....1..0
..1..2....0..1....2..0....2..1....1..2....0..3....3..2....3..2....1..3....2..1
..3..1....2..3....3..1....3..2....3..1....1..0....1..3....0..1....2..1....3..0
..2..0....1..2....0..2....1..0....2..3....2..3....2..1....3..2....3..0....1..2
..3..2....0..3....1..3....2..3....1..0....1..2....3..2....0..1....2..1....3..1

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

Column 2 of A232161.

Empirical: a(n) = 4*a(n-1) + 2*a(n-2) - 13*a(n-3) - 5*a(n-4) + 14*a(n-5) - 3*a(n-6) + 3*a(n-7) + 8*a(n-8) + a(n-9) - a(n-10) for n>11.

Empirical g.f.: 2*x*(1 + 5*x - 7*x^2 - 20*x^3 - 3*x^4 + 24*x^5 + 5*x^6 + 7*x^7 + 15*x^8 + 2*x^9 - 2*x^10) / (1 - 4*x - 2*x^2 + 13*x^3 + 5*x^4 - 14*x^5 + 3*x^6 - 3*x^7 - 8*x^8 - x^9 + x^10). - Colin Barker, Oct 03 2018

A232156 Number of nX3 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, vertically or antidiagonally, and no adjacent values equal.

Original entry on oeis.org

4, 62, 290, 1284, 5902, 27086, 124436, 572080, 2629946, 12090710, 55591878, 255589946, 1175154022, 5403111082, 24842308392, 114220099740, 525160514282, 2414582116408, 11101765510580, 51043677955498, 234688597761528

Offset: 1

R. H. Hardin, Nov 19 2013

nonn

Column 3 of A232161

			Some solutions for n=7
..1..2..3....1..2..3....0..1..2....1..2..3....2..1..0....0..3..1....2..1..2
..3..1..0....3..1..2....2..0..3....3..0..1....3..2..1....1..2..0....3..0..3
..0..3..2....2..0..3....3..2..1....1..2..0....1..0..2....0..3..2....1..2..1
..2..0..1....3..1..2....1..0..3....0..3..2....2..3..0....2..0..3....3..0..2
..1..3..0....2..3..0....3..2..1....2..0..3....1..2..1....1..2..0....2..3..0
..0..2..1....1..2..1....0..3..0....3..1..2....0..3..0....3..1..3....0..1..2
..3..0..3....0..3..0....1..2..1....0..3..1....2..1..3....2..0..2....2..3..1

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

Empirical: a(n) = 8*a(n-1) -12*a(n-2) -33*a(n-3) +40*a(n-4) +286*a(n-5) -545*a(n-6) -642*a(n-7) +2651*a(n-8) -1783*a(n-9) -2378*a(n-10) +4407*a(n-11) -1301*a(n-12) -2857*a(n-13) +3373*a(n-14) +157*a(n-15) -2558*a(n-16) +366*a(n-17) +1084*a(n-18) +818*a(n-19) -2988*a(n-20) -2028*a(n-21) +2529*a(n-22) +1294*a(n-23) +328*a(n-24) +582*a(n-25) -122*a(n-26) -180*a(n-27) +47*a(n-28) +21*a(n-29) -3*a(n-30) for n>33

A232157 Number of nX4 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, vertically or antidiagonally, and no adjacent values equal.

Original entry on oeis.org

8, 218, 1284, 7770, 46702, 286770, 1767266, 10830650, 66701686, 410364610, 2522566124, 15524673872, 95489164864, 587352257166, 3613537440642, 22227593479382, 136734516680534, 841147631122416, 5174280907720634

Offset: 1

R. H. Hardin, Nov 19 2013

nonn

Column 4 of A232161

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 94

Empirical recurrence of order 94 (see link above)

A232158 Number of nX5 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, vertically or antidiagonally, and no adjacent values equal.

Original entry on oeis.org

14, 746, 5902, 46702, 382996, 3183932, 26694774, 223026806, 1869037596, 15673051556, 131274639250, 1100535460668, 9225695626046, 77312726353080, 648103682234572, 5432428499191068, 45531948090605296, 381665246488467802

Offset: 1

R. H. Hardin, Nov 19 2013

nonn

Column 5 of A232161

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

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

A232159 Number of nX6 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, vertically or antidiagonally, and no adjacent values equal.

Original entry on oeis.org

26, 2600, 27086, 286770, 3183932, 36275078, 415332300, 4764939084, 54785401618, 629979277720, 7246595856072, 83366908500616, 959177256873984, 11035264357800498, 126966562329855518, 1460839965204197890

Offset: 1

R. H. Hardin, Nov 19 2013

nonn

Column 6 of A232161

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

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

A232160 Number of nX7 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, vertically or antidiagonally, and no adjacent values equal.

Original entry on oeis.org

48, 9004, 124436, 1767266, 26694774, 415332300, 6564512068, 103384156384, 1636124088162, 25973583237174, 411171410014356, 6519608941018384, 103473233282931542, 1639791299611784558, 26009017324816484476

Offset: 1

R. H. Hardin, Nov 19 2013

nonn

Column 7 of A232161

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

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

A232154 Number of n X n 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, vertically or antidiagonally, and no adjacent values equal.

Original entry on oeis.org

1, 18, 290, 7770, 382996, 36275078, 6564512068, 2246994465516, 1482101422338982, 1881388287368571956

Offset: 1

R. H. Hardin, Nov 19 2013

nonn

Diagonal of A232161

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

cp's OEIS Frontend

A232155 Number of n X 2 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, vertically or antidiagonally, and no adjacent values equal.

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A232156 Number of nX3 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, vertically or antidiagonally, and no adjacent values equal.

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A232157 Number of nX4 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, vertically or antidiagonally, and no adjacent values equal.

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A232158 Number of nX5 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, vertically or antidiagonally, and no adjacent values equal.

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A232159 Number of nX6 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, vertically or antidiagonally, and no adjacent values equal.

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A232160 Number of nX7 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, vertically or antidiagonally, and no adjacent values equal.

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A232154 Number of n X n 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, vertically or antidiagonally, and no adjacent values equal.

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