A268766 -id:A268766 - cp's OEIS frontend

A268760 Number of n X n binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

0, 6, 56, 1148, 32056, 1552272, 127676872, 18045771274, 4495138018796, 1955829240647962, 1511334747222697904, 2064152526111916503300, 5022957354228609008158500, 21748481726801956896608976098

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Diagonal of A268766.

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

R. H. Hardin, Table of n, a(n) for n = 1..26

Cf. A268766.

A268761 Number of n X 3 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

2, 15, 56, 223, 762, 2607, 8500, 27411, 86622, 270955, 838224, 2573015, 7841538, 23759463, 71619436, 214933915, 642504870, 1914023267, 5684288136, 16834582623, 49732758858, 146587890015, 431177727396, 1265883329827, 3710027613934

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

			Some solutions for n=4:
..1..0..1. .0..1..1. .1..0..0. .1..0..1. .0..1..0. .1..1..0. .0..0..0
..0..0..1. .0..0..0. .0..0..0. .0..0..0. .0..0..1. .0..0..0. .0..0..0
..0..0..0. .0..0..0. .1..0..1. .0..1..0. .0..0..0. .0..0..0. .1..0..1
..0..0..0. .0..0..0. .0..0..1. .0..0..1. .0..0..1. .0..1..0. .1..0..0

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

Column 3 of A268766.

Empirical: a(n) = 4*a(n-1) + 2*a(n-2) - 16*a(n-3) - a(n-4) + 12*a(n-5) - 4*a(n-6).

Empirical g.f.: x*(2 + 7*x - 8*x^2 + x^3) / (1 - 2*x - 3*x^2 + 2*x^3)^2. - Colin Barker, Jan 14 2019

A268762 Number of n X 4 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

5, 44, 223, 1148, 5170, 23156, 99057, 418924, 1736105, 7122856, 28898144, 116346184, 465034573, 1848051516, 7306228767, 28758043956, 112751067666, 440538622908, 1715952146561, 6665380161836, 25826102521633, 99840968906384

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

			Some solutions for n=4:
..1..0..0..0. .1..0..0..0. .1..0..1..0. .0..0..0..1. .0..0..1..0
..0..0..0..0. .0..0..1..1. .0..0..0..0. .1..0..0..0. .0..0..0..0
..1..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..1. .0..0..1..1
..1..0..0..1. .1..0..0..1. .0..0..1..0. .0..0..0..1. .1..0..0..0

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

Column 4 of A268766.

Empirical: a(n) = 4*a(n-1) + 10*a(n-2) - 32*a(n-3) - 47*a(n-4) + 40*a(n-5) + 38*a(n-6) - 12*a(n-7) - 9*a(n-8).

Empirical g.f.: x*(5 + 24*x - 3*x^2 - 24*x^3 - 9*x^4) / (1 - 2*x - 7*x^2 + 2*x^3 + 3*x^4)^2. - Colin Barker, Jan 14 2019

A268763 Number of nX5 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

10, 105, 762, 5170, 32056, 193573, 1129042, 6475898, 36505596, 203462597, 1122256900, 6140903312, 33367393732, 180252797855, 968778729426, 5183858768244, 27630592631158, 146768594783741, 777214421588348

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 5 of A268766.

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

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

Cf. A268766.

Empirical: a(n) = 4*a(n-1) +28*a(n-2) -62*a(n-3) -314*a(n-4) +78*a(n-5) +867*a(n-6) +6*a(n-7) -859*a(n-8) +46*a(n-9) +215*a(n-10) -8*a(n-11) -16*a(n-12)

A268764 Number of nX6 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

20, 258, 2607, 23156, 193573, 1552272, 12111209, 92571436, 696659613, 5178525870, 38112289517, 278191828634, 2016589831189, 14532118028260, 104191269908219, 743719988895596, 5288057396240333, 37470071363668612, 264689231027772351

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 6 of A268766.

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

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

Cf. A268766.

Empirical: a(n) = 6*a(n-1) +51*a(n-2) -214*a(n-3) -1074*a(n-4) +2018*a(n-5) +7713*a(n-6) -10572*a(n-7) -22926*a(n-8) +30116*a(n-9) +25283*a(n-10) -32400*a(n-11) -15148*a(n-12) +15184*a(n-13) +5660*a(n-14) -2688*a(n-15) -1024*a(n-16)

A268765 Number of nX7 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

38, 595, 8500, 99057, 1129042, 12111209, 127676872, 1312123185, 13311824510, 133228716170, 1321110678618, 12988699400546, 126844585914726, 1231361200765123, 11893679949360102, 114371480492930683

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 7 of A268766.

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

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

Cf. A268766.

Empirical: a(n) = 12*a(n-1) +64*a(n-2) -942*a(n-3) -1476*a(n-4) +26868*a(n-5) +2249*a(n-6) -376788*a(n-7) +333472*a(n-8) +2686292*a(n-9) -4376424*a(n-10) -8985248*a(n-11) +21881197*a(n-12) +12658940*a(n-13) -55768960*a(n-14) +923990*a(n-15) +80699088*a(n-16) -25850884*a(n-17) -69171189*a(n-18) +34934900*a(n-19) +34833816*a(n-20) -22502076*a(n-21) -9502460*a(n-22) +7752808*a(n-23) +1023260*a(n-24) -1356480*a(n-25) +55136*a(n-26) +94080*a(n-27) -14400*a(n-28)

cp's OEIS Frontend

A268760 Number of n X n binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A268761 Number of n X 3 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A268762 Number of n X 4 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A268763 Number of nX5 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A268764 Number of nX6 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A268765 Number of nX7 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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