A268740 -id:A268740 - cp's OEIS frontend

A268734 Number of n X n binary arrays with some 1 horizontally or vertically adjacent to some other 1 exactly once.

0, 4, 80, 2876, 200204, 29134076, 9039552112, 6084192150856, 8965720251221240, 29122359898196696856, 209490003763160695865576, 3348908247850171650090422060, 119286836904111393911302107179212

Offset: 1

R. H. Hardin, Feb 12 2016

nonn

Diagonal of A268740.

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

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

Cf. A268740.

A268735 Number of n X 3 binary arrays with some 1 horizontally or vertically adjacent to some other 1 exactly once.

Original entry on oeis.org

2, 15, 80, 396, 1788, 7831, 33170, 137868, 563486, 2275119, 9091772, 36031648, 141793168, 554669335, 2158604934, 8363066408, 32273565050, 124112115647, 475807505288, 1819019281732, 6936664653476, 26392068734023, 100206016839642

Offset: 1

R. H. Hardin, Feb 12 2016

nonn

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

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

Column 3 of A268740.

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*(2 + 7*x + 4*x^2 + 4*x^3 - 7*x^5 + 2*x^6) / (1 - 2*x - 6*x^2 + x^4)^2. - Colin Barker, Jan 14 2019

A268736 Number of nX4 binary arrays with some 1 horizontally or vertically adjacent to some other 1 exactly once.

Original entry on oeis.org

5, 48, 396, 2876, 19591, 128232, 816009, 5087814, 31228804, 189328186, 1136393919, 6764778660, 39991075367, 235019630164, 1374139675314, 7998875575940, 46380134987289, 267999333435856, 1543818690094499, 8868640131544198

Offset: 1

R. H. Hardin, Feb 12 2016

nonn

Column 4 of A268740.

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

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

Cf. A268740.

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)

A268737 Number of nX5 binary arrays with some 1 horizontally or vertically adjacent to some other 1 exactly once.

Original entry on oeis.org

10, 145, 1788, 19591, 200204, 1971414, 18847982, 176668038, 1629738420, 14851460143, 133983018272, 1198816726867, 10652116047394, 94092052069550, 826903484125628, 7234834159717064, 63053215344757166, 547626807437714177

Offset: 1

R. H. Hardin, Feb 12 2016

nonn

Column 5 of A268740.

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

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

Cf. A268740.

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)

A268738 Number of nX6 binary arrays with some 1 horizontally or vertically adjacent to some other 1 exactly once.

Original entry on oeis.org

20, 420, 7831, 128232, 1971414, 29134076, 418632185, 5894815754, 81718671716, 1119014223138, 15171181272721, 203998929406004, 2724149465085496, 36163754541884778, 477648079847735215, 6280858615510607492

Offset: 1

R. H. Hardin, Feb 12 2016

nonn

Column 6 of A268740.

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

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

Cf. A268740.

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)

A268739 Number of nX7 binary arrays with some 1 horizontally or vertically adjacent to some other 1 exactly once.

Original entry on oeis.org

38, 1183, 33170, 816009, 18847982, 418632185, 9039552112, 191307160577, 3985770068310, 82030747371058, 1671509767296774, 33781019022038039, 678004335124666334, 13528033902348727292, 268553181861956273470

Offset: 1

R. H. Hardin, Feb 12 2016

nonn

Column 7 of A268740.

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

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

Cf. A268740.

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

A268734 Number of n X n binary arrays with some 1 horizontally or vertically adjacent to some other 1 exactly once.

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A268735 Number of n X 3 binary arrays with some 1 horizontally or vertically adjacent to some other 1 exactly once.

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A268736 Number of nX4 binary arrays with some 1 horizontally or vertically adjacent to some other 1 exactly once.

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A268737 Number of nX5 binary arrays with some 1 horizontally or vertically adjacent to some other 1 exactly once.

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A268738 Number of nX6 binary arrays with some 1 horizontally or vertically adjacent to some other 1 exactly once.

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A268739 Number of nX7 binary arrays with some 1 horizontally or vertically adjacent to some other 1 exactly once.

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