A269075 -id:A269075 - cp's OEIS frontend

A269069 Number of n X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

2, 11, 123, 3288, 165607, 18220241, 4064720816, 1833956006577, 1778703508587227, 3374673365461249568, 14101540722268888633757, 114651904507399541002097761, 2060026489521744559823250922304, 72580676762280474254836112626897875

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Diagonal of A269075.

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

R. H. Hardin, Table of n, a(n) for n = 1..23

Cf. A269075.

A269070 Number of n X 3 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

7, 27, 123, 537, 2343, 10167, 43959, 189465, 814359, 3491691, 14937987, 63778065, 271799175, 1156345287, 4911870063, 20834207313, 88251723687, 373358554971, 1577691954507, 6659543294313, 28081651307943, 118299768626103

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

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

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

Column 3 of A269075.

Empirical: a(n) = 10*a(n-1) - 31*a(n-2) + 24*a(n-3) + 21*a(n-4) - 18*a(n-5) - 9*a(n-6).

Empirical g.f.: x*(7 - 43*x + 70*x^2 - 24*x^3 - 9*x^4 - 9*x^5) / (1 - 5*x + 3*x^2 + 3*x^3)^2. - Colin Barker, Jan 18 2019

A269071 Number of n X 4 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

13, 76, 521, 3288, 20400, 123976, 742688, 4397376, 25791040, 150081504, 867569920, 4986765312, 28523566592, 162453499008, 921756644864, 5212543265792, 29388948548608, 165253519908352, 926962234179584, 5188178346090496

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

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

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

Column 4 of A269075.

Empirical: a(n) = 12*a(n-1) - 40*a(n-2) + 8*a(n-3) + 92*a(n-4) - 32*a(n-5) - 64*a(n-6) for n>7.

Empirical g.f.: x*(13 - 80*x + 129*x^2 - 28*x^3 - 20*x^4 - 48*x^5 + 4*x^6) / (1 - 6*x + 2*x^2 + 8*x^3)^2. - Colin Barker, Jan 18 2019

A269072 Number of nX5 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

23, 185, 1887, 17713, 165607, 1529241, 14011359, 127528641, 1154377943, 10400164377, 93314875007, 834244316721, 7434343205095, 66061046189497, 585498663953471, 5177144091416833, 45680435610848791, 402277442193052665

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 5 of A269075.

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

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

Cf. A269075.

Empirical: a(n) = 24*a(n-1) -198*a(n-2) +584*a(n-3) +137*a(n-4) -2864*a(n-5) +1132*a(n-6) +4336*a(n-7) -1391*a(n-8) -2280*a(n-9) +90*a(n-10) +200*a(n-11) -25*a(n-12)

A269073 Number of nX6 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

41, 489, 7477, 102545, 1383105, 18220241, 236272677, 3024972401, 38333973609, 481701017577, 6010309951205, 74542025956769, 919716929870465, 11296618314880209, 138204770920790229, 1684906034464128193

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 6 of A269075.

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

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

Cf. A269075.

Empirical: a(n) = 28*a(n-1) -230*a(n-2) +192*a(n-3) +3805*a(n-4) -5776*a(n-5) -27808*a(n-6) +25744*a(n-7) +101333*a(n-8) -13916*a(n-9) -149690*a(n-10) -66848*a(n-11) +23183*a(n-12) +9888*a(n-13) -2304*a(n-14)

A269074 Number of nX7 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

72, 1204, 27042, 542112, 10778640, 210476400, 4064720816, 77785162880, 1477636398784, 27897108860960, 523921783242624, 9794822341611072, 182387895832407680, 3384281324193062016, 62600172035227164032

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 7 of A269075.

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

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

Cf. A269075.

Empirical: a(n) = 60*a(n-1) -1352*a(n-2) +13344*a(n-3) -35948*a(n-4) -311480*a(n-5) +1985472*a(n-6) +1821840*a(n-7) -31021776*a(n-8) +4125984*a(n-9) +251967152*a(n-10) -46853056*a(n-11) -1173410880*a(n-12) -138650624*a(n-13) +2912101888*a(n-14) +1295316992*a(n-15) -3360870400*a(n-16) -2339016704*a(n-17) +1368141824*a(n-18) +1168457728*a(n-19) -291553280*a(n-20) -245170176*a(n-21) +45023232*a(n-22) +19922944*a(n-23) -4194304*a(n-24) for n>25

A269076 Number of 2 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

4, 11, 27, 76, 185, 489, 1204, 3059, 7539, 18748, 46001, 112977, 275620, 671387, 1629003, 3944428, 9524969, 22955577, 55208404, 132545027, 317673891, 760222300, 1816668257, 4335499425, 10333941316, 24603369515, 58513434747, 139020574348

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

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

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

Row 2 of A269075.

Empirical: a(n) = 2*a(n-1) + 5*a(n-2) - 6*a(n-3) - 9*a(n-4).

Empirical g.f.: x*(4 + 3*x - 15*x^2 - 9*x^3) / (1 - x - 3*x^2)^2. - Colin Barker, Jan 18 2019

A269077 Number of 3 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

8, 32, 123, 521, 1887, 7477, 27042, 102070, 368391, 1351259, 4850557, 17489481, 62373468, 222422348, 788291635, 2789267661, 9831173339, 34583332541, 121320954422, 424799241314, 1484281289599, 5177412026719, 18028809567225

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

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

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

Row 3 of A269075.

Empirical: a(n) = 4*a(n-1) + 8*a(n-2) - 34*a(n-3) - 16*a(n-4) + 60*a(n-5) - 25*a(n-6).

Empirical g.f.: x*(8 - 69*x^2 + 45*x^3 + 35*x^4 - 25*x^5) / (1 - 2*x - 6*x^2 + 5*x^3)^2. - Colin Barker, Jan 18 2019

A269078 Number of 4 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

16, 89, 537, 3288, 17713, 102545, 542112, 2991561, 15699273, 84015848, 437869217, 2298582593, 11896438960, 61665786297, 317089210745, 1629210973432, 8329629544721, 42518834195697, 216316340106688, 1098583548812969

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

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

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

Row 4 of A269075.

Empirical: a(n) = 4*a(n-1) + 28*a(n-2) - 78*a(n-3) - 264*a(n-4) + 296*a(n-5) + 527*a(n-6) - 252*a(n-7) - 324*a(n-8).

Empirical g.f.: x*(16 + 25*x - 267*x^2 - 104*x^3 + 691*x^4 + 275*x^5 - 576*x^6 - 324*x^7) / (1 - 2*x - 16*x^2 + 7*x^3 + 18*x^4)^2. - Colin Barker, Jan 19 2019

A269079 Number of 5Xn binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

32, 244, 2343, 20400, 165607, 1383105, 10778640, 86308622, 661641931, 5146079168, 39031235709, 297777942033, 2239241624640, 16861326990168, 125878250277823, 939067269600080, 6967653661432115, 51619835791134129, 381021973991495280

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Row 5 of A269075.

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

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

Cf. A269075.

Empirical: a(n) = 8*a(n-1) +52*a(n-2) -424*a(n-3) -816*a(n-4) +6756*a(n-5) +1362*a(n-6) -38476*a(n-7) +19016*a(n-8) +82920*a(n-9) -70008*a(n-10) -50556*a(n-11) +50607*a(n-12) +9180*a(n-13) -10404*a(n-14)

cp's OEIS Frontend

A269069 Number of n X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269070 Number of n X 3 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269071 Number of n X 4 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269072 Number of nX5 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269073 Number of nX6 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269074 Number of nX7 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269076 Number of 2 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269077 Number of 3 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269078 Number of 4 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269079 Number of 5Xn binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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