A318343 -id:A318343 - cp's OEIS frontend

A318337 Number of n X n 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 6, 20, 67, 393, 4133, 86487, 3590263, 285034170, 43174729552, 12383193287684, 6712873423988949, 6871475875643572553, 13272675681120501977922, 48367944991570243925176462, 332490278773637201581189154380

Offset: 1

R. H. Hardin, Aug 24 2018

nonn

Diagonal of A318343.

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

R. H. Hardin, Table of n, a(n) for n = 1..17

Cf. A318343.

A318338 Number of nX3 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

4, 10, 20, 36, 76, 160, 344, 748, 1624, 3544, 7724, 16856, 36776, 80252, 175128, 382168, 833996, 1819992, 3971720, 8667356, 18914520, 41276600, 90076716, 196571800, 428972904, 936135100, 2042900376, 4458162072, 9728917388

Offset: 1

R. H. Hardin, Aug 24 2018

nonn

Column 3 of A318343.

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

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

Cf. A318343.

Empirical: a(n) = 2*a(n-1) +2*a(n-2) -3*a(n-3) -2*a(n-4) +2*a(n-5) for n>6

A318339 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 20, 36, 67, 148, 343, 817, 1975, 4788, 11644, 28327, 68949, 167840, 408591, 994711, 2421617, 5895464, 14352589, 34941627, 85066013, 207094729, 504175889, 1227425339, 2988189330, 7274801283, 17710636103, 43116865936, 104968794797

Offset: 1

R. H. Hardin, Aug 24 2018

nonn

Column 4 of A318343.

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

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

Cf. A318343.

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

A318340 Number of nX5 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

16, 42, 76, 148, 393, 1115, 3321, 10111, 30943, 95244, 293401, 904986, 2792217, 8617223, 26597072, 82096253, 253412398, 782236683, 2414640760, 7453642765, 23008358869, 71023687464, 219240636280, 676766784339, 2089089700480

Offset: 1

R. H. Hardin, Aug 24 2018

nonn

Column 5 of A318343.

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

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

Cf. A318343.

Empirical: a(n) = 3*a(n-1) +5*a(n-2) -12*a(n-3) -17*a(n-4) +20*a(n-5) +31*a(n-6) -13*a(n-7) -33*a(n-8) +a(n-9) +20*a(n-10) +2*a(n-11) -4*a(n-12) -3*a(n-13) +a(n-15) for n>18

A318341 Number of nX6 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

32, 89, 160, 343, 1115, 4133, 16267, 66070, 270320, 1112195, 4584060, 18912384, 78063418, 322286580, 1330722690, 5494862763, 22690219542, 93697259411, 386917457753, 1597759628888, 6597895365718, 27245818039527, 112510877313046

Offset: 1

R. H. Hardin, Aug 24 2018

nonn

Column 6 of A318343.

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

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

Cf. A318343.

Empirical: a(n) = 4*a(n-1) +9*a(n-2) -28*a(n-3) -57*a(n-4) +78*a(n-5) +199*a(n-6) -73*a(n-7) -366*a(n-8) -89*a(n-9) +336*a(n-10) +298*a(n-11) -42*a(n-12) -362*a(n-13) -234*a(n-14) +215*a(n-15) +227*a(n-16) +16*a(n-17) -99*a(n-18) -65*a(n-19) +7*a(n-20) +27*a(n-21) +4*a(n-22) -4*a(n-23) for n>27

A318342 Number of nX7 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

64, 190, 344, 817, 3321, 16267, 86487, 476348, 2647555, 14797928, 82863837, 464502820, 2605038853, 14613251568, 81984567828, 459986291171, 2580903334169, 14481247495703, 81253869292071, 455915278972371, 2558145839414926

Offset: 1

R. H. Hardin, Aug 24 2018

nonn

Column 7 of A318343.

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

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

Cf. A318343.

Empirical: a(n) = 6*a(n-1) +15*a(n-2) -89*a(n-3) -165*a(n-4) +555*a(n-5) +1215*a(n-6) -1671*a(n-7) -5290*a(n-8) +1469*a(n-9) +13428*a(n-10) +5625*a(n-11) -17967*a(n-12) -19967*a(n-13) +3366*a(n-14) +22938*a(n-15) +28588*a(n-16) +12646*a(n-17) -41780*a(n-18) -75067*a(n-19) +9433*a(n-20) +89071*a(n-21) +52784*a(n-22) -43392*a(n-23) -74658*a(n-24) -40*a(n-25) +41248*a(n-26) +12244*a(n-27) -12324*a(n-28) -4868*a(n-29) +3028*a(n-30) +660*a(n-31) -1352*a(n-32) -152*a(n-33) +496*a(n-34) +32*a(n-35) -64*a(n-36) for n>41

cp's OEIS Frontend

A318337 Number of n X n 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

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A318338 Number of nX3 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

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A318339 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

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A318340 Number of nX5 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

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A318341 Number of nX6 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

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A318342 Number of nX7 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

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Comments

Examples

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