A268750 -id:A268750 - cp's OEIS frontend

A268744 Number of n X 2 binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

4, 11, 32, 89, 244, 659, 1760, 4657, 12228, 31899, 82752, 213641, 549236, 1406755, 3591232, 9140833, 23204612, 58765099, 148496608, 374496953, 942729588, 2369172915, 5944748064, 14895231121, 37272007108, 93149401019, 232527917312

Offset: 1

R. H. Hardin, Feb 12 2016

nonn

Column 2 of A268750.

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

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

Cf. A268750.

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 4*a(n-3) - a(n-4).

Empirical g.f.: x*(4 - 5*x - 4*x^2 - x^3) / (1 - 2*x - x^2)^2. - Colin Barker, Mar 21 2018

A268743 Number of n X n binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

Original entry on oeis.org

2, 11, 143, 4110, 255651, 34732937, 10319681062, 6744840113811, 9736268648482947, 31152408949342676906, 221573405414594347811555, 3511390061199964238627005057, 124222798189336185449669887550302

Offset: 1

R. H. Hardin, Feb 12 2016

nonn

Diagonal of A268750.

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

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

Cf. A268750.

A268745 Number of n X 3 binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

Original entry on oeis.org

7, 32, 143, 623, 2615, 10830, 44067, 177429, 707163, 2796840, 10986379, 42911627, 166777091, 645395334, 2488065863, 9559464281, 36618142447, 139888931680, 533099140807, 2027067051095, 7692165427919, 29135580083054, 110168752548843

Offset: 1

R. H. Hardin, Feb 12 2016

nonn

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

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

Column 3 of A268750.

Empirical: a(n) = 4*a(n-1) + 8*a(n-2) - 24*a(n-3) - 38*a(n-4) + 4*a(n-5) + 12*a(n-6) - a(n-8).

Empirical g.f.: x*(7 + 4*x - 41*x^2 - 37*x^3 + 13*x^4 + 6*x^5 + x^6 - x^7) / (1 - 2*x - 6*x^2 + x^4)^2. - Colin Barker, Jan 14 2019

A268746 Number of nX4 binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

Original entry on oeis.org

13, 89, 623, 4110, 26334, 165019, 1016807, 6183665, 37209717, 221970102, 1314544140, 7737069617, 45297553803, 263980824665, 1532201345489, 8861529601362, 51088246525260, 293694819166095, 1684057081243885

Offset: 1

R. H. Hardin, Feb 12 2016

nonn

Column 4 of A268750.

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

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

Cf. A268750.

Empirical: a(n) = 8*a(n-1) +2*a(n-2) -82*a(n-3) -49*a(n-4) +124*a(n-5) +39*a(n-6) -58*a(n-7) -6*a(n-8) +8*a(n-9) -a(n-10)

A268747 Number of nX5 binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

Original entry on oeis.org

23, 244, 2615, 26334, 255651, 2425799, 22577073, 207252725, 1880654551, 16909709308, 150867667407, 1337324783132, 11788337576943, 103412756868981, 903363696442081, 7862056896605875, 68198486775427551, 589834799847933624

Offset: 1

R. H. Hardin, Feb 12 2016

nonn

Column 5 of A268750.

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

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

Cf. A268750.

Empirical: a(n) = 8*a(n-1) +56*a(n-2) -288*a(n-3) -1506*a(n-4) +870*a(n-5) +7568*a(n-6) -1632*a(n-7) -15481*a(n-8) +4624*a(n-9) +13495*a(n-10) -6192*a(n-11) -4336*a(n-12) +2890*a(n-13) +82*a(n-14) -288*a(n-15) +24*a(n-16) +8*a(n-17) -a(n-18)

A268748 Number of nX6 binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

Original entry on oeis.org

41, 659, 10830, 165019, 2425799, 34732937, 487682438, 6746117783, 92215499119, 1248437108837, 16766958502992, 223674635599161, 2966748789292217, 39154974765661223, 514529476985579624, 6735601878829825279

Offset: 1

R. H. Hardin, Feb 12 2016

nonn

Column 6 of A268750.

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

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

Cf. A268750.

Empirical: a(n) = 16*a(n-1) +60*a(n-2) -1148*a(n-3) -3346*a(n-4) +16272*a(n-5) +36588*a(n-6) -104246*a(n-7) -147989*a(n-8) +349140*a(n-9) +217324*a(n-10) -591448*a(n-11) -19320*a(n-12) +431032*a(n-13) -151921*a(n-14) -73194*a(n-15) +41684*a(n-16) +2552*a(n-17) -3594*a(n-18) +148*a(n-19) +100*a(n-20) -4*a(n-21) -a(n-22)

A268749 Number of nX7 binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

Original entry on oeis.org

72, 1760, 44067, 1016807, 22577073, 487682438, 10319681062, 215027310572, 4425392044505, 90177748184504, 1822495416470859, 36579128848735042, 729860195814419706, 14489046573912834959, 286363070886993749567

Offset: 1

R. H. Hardin, Feb 12 2016

nonn

Column 7 of A268750.

			Some solutions for n=3
..0..0..1..0..1..0..0. .0..1..1..0..1..0..0. .0..0..0..0..0..1..0
..1..0..0..1..0..1..0. .0..0..0..0..0..0..1. .0..1..0..1..0..1..0
..0..0..1..0..0..1..0. .0..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. A268750.

Empirical: a(n) = 18*a(n-1) +325*a(n-2) -4074*a(n-3) -48747*a(n-4) +201072*a(n-5) +2225020*a(n-6) -6248320*a(n-7) -47573325*a(n-8) +135873052*a(n-9) +512366407*a(n-10) -1794441336*a(n-11) -2517416282*a(n-12) +13453431136*a(n-13) +1270823811*a(n-14) -55187301646*a(n-15) +38695555999*a(n-16) +115237077158*a(n-17) -158181613013*a(n-18) -96178246900*a(n-19) +263575852534*a(n-20) -18739881048*a(n-21) -224653932202*a(n-22) +90835575680*a(n-23) +105290165907*a(n-24) -69076575582*a(n-25) -27720217521*a(n-26) +26811874806*a(n-27) +3877126783*a(n-28) -6197138172*a(n-29) -207452034*a(n-30) +895782500*a(n-31) -10034133*a(n-32) -81777708*a(n-33) +1520627*a(n-34) +4630616*a(n-35) -28132*a(n-36) -153828*a(n-37) -2195*a(n-38) +2658*a(n-39) +93*a(n-40) -18*a(n-41) -a(n-42)

cp's OEIS Frontend

A268744 Number of n X 2 binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

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A268743 Number of n X n binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

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A268745 Number of n X 3 binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

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A268746 Number of nX4 binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

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A268747 Number of nX5 binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

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A268748 Number of nX6 binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

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A268749 Number of nX7 binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

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