A268774 -id:A268774 - cp's OEIS frontend

A268767 Number of n X n 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

0, 12, 112, 2296, 64112, 3104544, 255353744, 36091542548, 8990276037592, 3911658481295924, 3022669494445395808, 4128305052223833006600, 10045914708457218016317000, 43496963453603913793217952196

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Diagonal of A268774.

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

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

Cf. A268774.

A268768 Number of n X 2 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

3, 12, 32, 100, 248, 620, 1456, 3380, 7656, 17148, 37920, 83140, 180824, 390796, 839824, 1796180, 3825352, 8116764, 17165568, 36195300, 76118840, 159694252, 334301552, 698429300, 1456510888, 3032326460, 6303262176, 13083742980

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

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

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

Column 2 of A268774.

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 4*a(n-4) for n>5.
Conjectures from Colin Barker, Jan 14 2019: (Start)
G.f.: x*(3 + 6*x - x^2 + 12*x^3 + 12*x^4) / ((1 + x)^2*(1 - 2*x)^2).
a(n) = (4/27)*(7*((-1)^n-2^n) + 3*((-1)^n + 2^(2+n))*n) for n>1.
(End)

A268769 Number of n X 3 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

12, 32, 112, 446, 1524, 5214, 17000, 54822, 173244, 541910, 1676448, 5146030, 15683076, 47518926, 143238872, 429867830, 1285009740, 3828046534, 11368576272, 33669165246, 99465517716, 293175780030, 862355454792, 2531766659654

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

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

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

Column 3 of A268774.

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) for n>8.

Empirical g.f.: 2*x*(6 - 8*x - 20*x^2 + 63*x^3 + 20*x^4 - 47*x^5 + 4*x^6 + 4*x^7) / (1 - 2*x - 3*x^2 + 2*x^3)^2. - Colin Barker, Jan 15 2019

A268770 Number of n X 4 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

36, 100, 446, 2296, 10340, 46312, 198114, 837848, 3472210, 14245712, 57796288, 232692368, 930069146, 3696103032, 14612457534, 57516087912, 225502135332, 881077245816, 3431904293122, 13330760323672, 51652205043266

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

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

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

Column 4 of A268774.

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) for n>10.

Empirical g.f.: 2*x*(18 - 22*x - 157*x^2 + 332*x^3 + 794*x^4 - 238*x^5 - 734*x^6 - 72*x^7 + 189*x^8 + 54*x^9) / (1 - 2*x - 7*x^2 + 2*x^3 + 3*x^4)^2. - Colin Barker, Jan 15 2019

A268771 Number of nX5 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

96, 248, 1524, 10340, 64112, 387146, 2258084, 12951796, 73011192, 406925194, 2244513800, 12281806624, 66734787464, 360505595710, 1937557458852, 10367717536488, 55261185262316, 293537189567482, 1554428843176696

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 5 of A268774.

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

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

Cf. A268774.

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) for n>14

A268772 Number of nX6 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

240, 620, 5214, 46312, 387146, 3104544, 24222418, 185142872, 1393319226, 10357051740, 76224579034, 556383657268, 4033179662378, 29064236056520, 208382539816438, 1487439977791192, 10576114792480666, 74940142727337224

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 6 of A268774.

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

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

Cf. A268774.

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) for n>18

A268773 Number of nX7 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

576, 1456, 17000, 198114, 2258084, 24222418, 255353744, 2624246370, 26623649020, 266457432340, 2642221357236, 25977398801092, 253689171829452, 2462722401530246, 23787359898720204, 228742960985861366

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 7 of A268774.

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

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

Cf. A268774.

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) for n>30

cp's OEIS Frontend

A268767 Number of n X n 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A268768 Number of n X 2 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A268769 Number of n X 3 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A268770 Number of n X 4 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A268771 Number of nX5 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A268772 Number of nX6 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A268773 Number of nX7 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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