A268886 -id:A268886 - cp's OEIS frontend

A268880 Number of n X n binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

0, 5, 84, 4133, 317966, 55491832, 19876401224, 15564645769042, 26617222097087230, 99905925686618815012, 832547140418699137884096, 15355865014207234684746438192, 632296902429868672596327438625296

Offset: 1

R. H. Hardin, Feb 15 2016

nonn

Diagonal of A268886.

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

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

Cf. A268886.

A268881 Number of n X 3 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

2, 14, 84, 462, 2418, 12252, 60666, 295230, 1417452, 6732102, 31690914, 148080468, 687592338, 3175567374, 14597507076, 66827528094, 304831251762, 1386004252620, 6283722000714, 28414577975934, 128187044049948, 577056144993366

Offset: 1

R. H. Hardin, Feb 15 2016

nonn

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

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

Column 3 of A268886.

Empirical: a(n) = 10*a(n-1) - 31*a(n-2) + 30*a(n-3) - 9*a(n-4).

Empirical g.f.: 2*x*(1 - 2*x)*(1 - x + x^2) / (1 - 5*x + 3*x^2)^2. - Colin Barker, Jan 15 2019

A268882 Number of n X 4 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

5, 54, 501, 4133, 31956, 236960, 1706732, 12034000, 83485488, 571836176, 3876692480, 26059576704, 173934499008, 1153927868416, 7615733792000, 50035609197824, 327432063642624, 2135189929320448, 13880060602788864

Offset: 1

R. H. Hardin, Feb 15 2016

nonn

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

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

Column 4 of A268886.

Empirical: a(n) = 16*a(n-1) - 88*a(n-2) + 200*a(n-3) - 208*a(n-4) + 96*a(n-5) - 16*a(n-6) for n>7.

Empirical g.f.: x*(5 - 26*x + 77*x^2 - 131*x^3 + 156*x^4 - 80*x^5 + 4*x^6) / (1 - 8*x + 12*x^2 - 4*x^3)^2. - Colin Barker, Jan 15 2019

A268883 Number of nX5 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

10, 158, 2190, 27130, 317966, 3596174, 39670270, 429588382, 4585939726, 48401059362, 506108414670, 5251396681678, 54134020936742, 554930619106590, 5661171443312270, 57509255942550986, 582036972222995470

Offset: 1

R. H. Hardin, Feb 15 2016

nonn

Column 5 of A268886.

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

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

Cf. A268886.

Empirical: a(n) = 26*a(n-1) -241*a(n-2) +994*a(n-3) -2060*a(n-4) +2218*a(n-5) -1201*a(n-6) +290*a(n-7) -25*a(n-8) for n>9

A268884 Number of nX6 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

20, 475, 9996, 186732, 3283890, 55491832, 911930096, 14681855846, 232688402028, 3642322709900, 56444213311842, 867475989937560, 13239446101273360, 200865483664370358, 3031934392327858732, 45561723449682618252

Offset: 1

R. H. Hardin, Feb 15 2016

nonn

Column 6 of A268886.

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

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

Cf. A268886.

Empirical: a(n) = 42*a(n-1) -665*a(n-2) +5138*a(n-3) -21972*a(n-4) +55274*a(n-5) -83769*a(n-6) +76202*a(n-7) -40273*a(n-8) +11304*a(n-9) -1296*a(n-10) for n>12

A268885 Number of nX7 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

38, 1340, 42362, 1187838, 31427480, 800733668, 19876401224, 483987898760, 11611969197776, 275345016177616, 6466964539799840, 150689548401385312, 3487912674084234304, 80273121207141357120, 1838370376874099584640

Offset: 1

R. H. Hardin, Feb 15 2016

nonn

Column 7 of A268886.

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

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

Cf. A268886.

Empirical: a(n) = 68*a(n-1) -1804*a(n-2) +24560*a(n-3) -195400*a(n-4) +974752*a(n-5) -3171360*a(n-6) +6871936*a(n-7) -9999248*a(n-8) +9740096*a(n-9) -6250176*a(n-10) +2552576*a(n-11) -621824*a(n-12) +79872*a(n-13) -4096*a(n-14) for n>16

A268887 Number of 2 X n binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 5, 14, 54, 158, 475, 1340, 3740, 10204, 27521, 73354, 193842, 508346, 1324791, 3433720, 8858104, 22757432, 58253885, 148634502, 378142446, 959527766, 2429034323, 6135877428, 15469187604, 38929330452, 97806402617, 245354321666

Offset: 1

R. H. Hardin, Feb 15 2016

nonn

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

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

Row 2 of A268886.

Empirical: a(n) = 2*a(n-1) + 5*a(n-2) - 4*a(n-3) - 11*a(n-4) - 6*a(n-5) - a(n-6).

Empirical g.f.: x^2*(5 + 4*x + x^2) / ((1 + x)^2*(1 - 2*x - x^2)^2). - Colin Barker, Jan 15 2019

A268888 Number of 3 X n binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 20, 84, 501, 2190, 9996, 42362, 178400, 732378, 2974934, 11933578, 47466417, 187325260, 734639334, 2865135348, 11121381104, 42989239524, 165564387000, 635557701344, 2432620417837, 9286486715514, 35366757558512, 134400104565934

Offset: 1

R. H. Hardin, Feb 15 2016

nonn

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

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

Row 3 of A268886.

Empirical: a(n) = 3*a(n-1) + 12*a(n-2) - 16*a(n-3) - 62*a(n-4) - 34*a(n-5) + 16*a(n-6) + 12*a(n-7) - a(n-8) - a(n-9).

Empirical g.f.: x^2*(2 - x)*(10 + 17*x + 13*x^2 + 6*x^3 + 2*x^4) / ((1 + x)*(1 - 2*x - 6*x^2 + x^4)^2). - Colin Barker, Jan 15 2019

A268889 Number of 4Xn binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 71, 462, 4133, 27130, 186732, 1187838, 7529253, 46440962, 283673207, 1710265892, 10226321520, 60660804228, 357586190291, 2096177689750, 12229766790505, 71054027831574, 411303965509420, 2373090804832634

Offset: 1

R. H. Hardin, Feb 15 2016

nonn

Row 4 of A268886.

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

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

Cf. A268886.

Empirical: a(n) = 2*a(n-1) +39*a(n-2) +14*a(n-3) -482*a(n-4) -1102*a(n-5) -111*a(n-6) +1758*a(n-7) +982*a(n-8) -1114*a(n-9) -743*a(n-10) +394*a(n-11) +206*a(n-12) -90*a(n-13) -17*a(n-14) +10*a(n-15) -a(n-16)

A268890 Number of 5Xn binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 235, 2418, 31956, 317966, 3283890, 31427480, 299524050, 2777161184, 25505113994, 231143340184, 2077724593805, 18526267129268, 164165431218906, 1446558738555296, 12686251671077220, 110791183092125102

Offset: 1

R. H. Hardin, Feb 15 2016

nonn

Row 5 of A268886.

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

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

Cf. A268886.

Empirical: a(n) = 2*a(n-1) +97*a(n-2) +116*a(n-3) -2923*a(n-4) -10986*a(n-5) +4951*a(n-6) +72992*a(n-7) +36740*a(n-8) -223968*a(n-9) -159382*a(n-10) +423052*a(n-11) +256370*a(n-12) -539504*a(n-13) -176570*a(n-14) +450908*a(n-15) +6166*a(n-16) -217920*a(n-17) +57416*a(n-18) +45120*a(n-19) -25021*a(n-20) +562*a(n-21) +2089*a(n-22) -388*a(n-23) -31*a(n-24) +14*a(n-25) -a(n-26)

cp's OEIS Frontend

A268880 Number of n X n binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

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A268881 Number of n X 3 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

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A268882 Number of n X 4 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

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A268883 Number of nX5 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

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A268884 Number of nX6 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

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A268885 Number of nX7 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

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A268887 Number of 2 X n binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

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A268888 Number of 3 X n binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

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A268889 Number of 4Xn binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

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A268890 Number of 5Xn binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

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