A269011 -id:A269011 - cp's OEIS frontend

A269005 Number of n X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

0, 4, 46, 2136, 109058, 14382480, 3258530608, 1582785864320, 1554970236400402, 3055129067325800608, 12891237725516640144940, 106775629834644247372248448, 1932363567303596958505554161216, 68821810412730939070416537380998580

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

Diagonal of A269011.

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

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

Cf. A269011.

A269006 Number of n X 3 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

2, 8, 46, 224, 1066, 4952, 22654, 102416, 458674, 2038328, 8999374, 39512144, 172645498, 751190504, 3256354942, 14069557088, 60610482274, 260412843944, 1116181074286, 4773749750528, 20376053362762, 86813692172216

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

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

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

Column 3 of A269011.

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.: 2*x*(1 - x)*(1 - 3*x)*(1 - 2*x + 3*x^2) / (1 - 5*x + 3*x^2 + 3*x^3)^2. - Colin Barker, Jan 18 2019

A269007 Number of n X 4 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

5, 36, 305, 2136, 14240, 91048, 566656, 3456320, 20760192, 123186784, 723791744, 4218132480, 24414483712, 140486492800, 804321836032, 4584741088256, 26032741150720, 147311358346752, 831044097026048, 4675403505475584

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

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

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

Column 4 of A269011.

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*(5 - 24*x + 73*x^2 - 124*x^3 + 60*x^4 + 16*x^5 + 4*x^6) / (1 - 6*x + 2*x^2 + 8*x^3)^2. - Colin Barker, Jan 18 2019

A269008 Number of n X 5 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

10, 88, 1078, 10976, 109058, 1053432, 10002542, 93733440, 869397882, 7996744280, 73044076454, 663272676512, 5992284643698, 53897945082104, 482908211678430, 4311837258739840, 38381936117267690, 340717648957870424

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

Column 5 of A269011.

			Some solutions for n=4
..1..0..0..0..0. .0..0..0..0..1. .1..0..0..0..1. .0..0..0..0..1
..1..0..0..1..0. .0..1..0..1..0. .1..0..0..0..1. .0..1..0..0..1
..0..0..1..0..0. .0..1..0..0..0. .0..1..0..0..0. .0..0..0..1..0
..1..0..1..0..1. .0..1..0..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. A269011.

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).

A269009 Number of nX6 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

20, 272, 4948, 73568, 1049588, 14382480, 192100836, 2516546784, 32481770852, 414339126768, 5234937372516, 65617049910368, 816985376286500, 10114119489148976, 124593533629907540, 1528232910934667360

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

Column 6 of A269011.

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

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

Cf. A269011.

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)

A269010 Number of nX7 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

38, 696, 18210, 390064, 8134304, 164351184, 3258530608, 63679868768, 1230707111424, 23573013881888, 448188039743360, 8468276406290880, 159151109503787520, 2977237536021550208, 55469798154343791232

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

Column 7 of A269011.

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

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

Cf. A269011.

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

A269012 Number of 2 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 4, 8, 36, 88, 272, 696, 1900, 4856, 12588, 31792, 80288, 200304, 498004, 1229672, 3024948, 7407496, 18079664, 43980072, 106688956, 258132824, 623113020, 1500935776, 3608439104, 8659683552, 20747930788, 49635222728, 118576046148

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

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

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

Row 2 of A269011.

Empirical: a(n) = 2*a(n-1) + 5*a(n-2) - 6*a(n-3) - 9*a(n-4).
Conjectures from Colin Barker, Jan 18 2019: (Start)
G.f.: 4*x^2 / (1 - x - 3*x^2)^2.
a(n) = 4*(-((1/2)*(1+sqrt(13)))^n*(sqrt(13)-13*n) + ((1/2)*(1-sqrt(13)))^n*(sqrt(13)+13*n)) / 169.
(End)

A269013 Number of 3 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 15, 46, 305, 1078, 4948, 18210, 73277, 270458, 1026795, 3757996, 13847240, 50155940, 181596651, 651546278, 2331910405, 8300115170, 29460799452, 104176325510, 367430075801, 1292287850546, 4534933300095, 15878737307224

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

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

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

Row 3 of A269011.

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^2*(15 - 14*x + x^2) / (1 - 2*x - 6*x^2 + 5*x^3)^2. - Colin Barker, Jan 18 2019

A269014 Number of 4 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 48, 224, 2136, 10976, 73568, 390064, 2291728, 12190944, 67387784, 356115520, 1906181472, 9983123936, 52432319344, 272227610848, 1412208727736, 7276913394080, 37421599567712, 191604936958480, 978880041945808

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

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

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

Row 4 of A269011.

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.: 8*x^2*(6 + 4*x - 13*x^2 - 12*x^3) / (1 - 2*x - 16*x^2 + 7*x^3 + 18*x^4)^2. - Colin Barker, Jan 18 2019

A269015 Number of 5Xn binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 145, 1066, 14240, 109058, 1049588, 8134304, 69184207, 534525058, 4286305792, 32838001316, 255036784680, 1935580387968, 14746081110093, 110945210978202, 834598743197152, 6232287294972630, 46465158121063708, 344786403529703264

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

Row 5 of A269011.

			Some solutions for n=4
..0..0..0..0. .0..0..0..1. .1..0..0..1. .1..0..0..0. .1..0..1..0
..0..1..0..0. .0..0..0..1. .1..0..0..1. .0..1..0..0. .1..0..1..0
..0..0..0..0. .0..1..0..0. .0..1..0..0. .0..0..0..1. .1..0..0..1
..1..1..0..1. .1..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..1. .0..0..0..0. .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. A269011.

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

A269005 Number of n X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269006 Number of n X 3 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269007 Number of n X 4 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269008 Number of n X 5 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269009 Number of nX6 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269010 Number of nX7 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269012 Number of 2 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269013 Number of 3 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269014 Number of 4 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269015 Number of 5Xn binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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