A279134 -id:A279134 - cp's OEIS frontend

A279128 Number of n X 2 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

1, 0, 9, 34, 87, 194, 400, 790, 1511, 2830, 5213, 9484, 17080, 30508, 54117, 95434, 167443, 292486, 508912, 882402, 1525219, 2628886, 4519577, 7751888, 13267384, 22662360, 38639553, 65769394, 111771663, 189671306, 321421456, 543987118

Offset: 1

R. H. Hardin, Dec 06 2016

nonn

Column 2 of A279134.

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

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

Cf. A279134.

Empirical: a(n) = 5*a(n-1) - 7*a(n-2) - 2*a(n-3) + 10*a(n-4) - 2*a(n-5) - 5*a(n-6) + a(n-7) + a(n-8) for n>9.

Empirical g.f.: x*(1 - 5*x + 16*x^2 - 9*x^3 - 30*x^4 + 17*x^5 + 22*x^6 - x^7 - 9*x^8) / ((1 - x)^2*(1 - x - x^2)^3). - Colin Barker, Feb 26 2018

A279129 Number of nX3 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 9, 66, 256, 820, 2551, 7491, 21131, 57971, 155551, 409876, 1064002, 2727560, 6917391, 17381168, 43320628, 107203164, 263611545, 644549767, 1567944409, 3796630655, 9154650571, 21989697066, 52634342562, 125577952504, 298716701553

Offset: 1

R. H. Hardin, Dec 06 2016

nonn

Column 3 of A279134.

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

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

Cf. A279134.

Empirical: a(n) = 6*a(n-1) -11*a(n-2) +5*a(n-3) +a(n-5) +9*a(n-6) -6*a(n-7) +3*a(n-8) -5*a(n-9) -a(n-11) for n>17

A279130 Number of nX4 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

3, 34, 256, 1324, 6396, 30074, 129264, 535814, 2150797, 8418336, 32296969, 121849424, 453295302, 1666387390, 6063302940, 21865526486, 78234877789, 277985152886, 981636776095, 3447186735368, 12044802324840, 41894649008470

Offset: 1

R. H. Hardin, Dec 06 2016

nonn

Column 4 of A279134.

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

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

Cf. A279134.

Empirical: a(n) = 16*a(n-1) -108*a(n-2) +401*a(n-3) -893*a(n-4) +1179*a(n-5) -600*a(n-6) -1173*a(n-7) +3468*a(n-8) -5018*a(n-9) +6446*a(n-10) -8766*a(n-11) +8587*a(n-12) -1891*a(n-13) -12870*a(n-14) +29298*a(n-15) -31377*a(n-16) +26556*a(n-17) -29210*a(n-18) +21407*a(n-19) +1380*a(n-20) -39341*a(n-21) +76349*a(n-22) -59868*a(n-23) +31048*a(n-24) -37732*a(n-25) +23625*a(n-26) +13127*a(n-27) -35339*a(n-28) +40641*a(n-29) -26406*a(n-30) +5772*a(n-31) +6474*a(n-32) -9682*a(n-33) +6694*a(n-34) -2802*a(n-35) +369*a(n-36) +540*a(n-37) -513*a(n-38) +299*a(n-39) -116*a(n-40) +36*a(n-41) -7*a(n-42) +a(n-43) for n>50

A279131 Number of nX5 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

3, 87, 820, 6396, 47452, 316516, 2017028, 12376570, 73672888, 428568648, 2445310419, 13733337644, 76104228971, 416938845972, 2261749445562, 12163774256441, 64922115452637, 344182830696292, 1813720428133600

Offset: 1

R. H. Hardin, Dec 06 2016

nonn

Column 5 of A279134.

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

R. H. Hardin, Table of n, a(n) for n = 1..250
R. H. Hardin, Empirical recurrence of order 88

Cf. A279134.

Empirical recurrence of order 88 (see link above)

A279132 Number of nX6 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

9, 194, 2551, 30074, 316516, 3125600, 29410145, 266502710, 2346800921, 20197483932, 170598730850, 1418685012262, 11643287106767, 94486219877716, 759316584725697, 6050247921127698, 47847435523630798, 375876383561544262

Offset: 1

R. H. Hardin, Dec 06 2016

nonn

Column 6 of A279134.

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

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

Cf. A279134.

A279133 Number of nX7 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

15, 400, 7491, 129264, 2017028, 29410145, 409061044, 5488392521, 71618045798, 913912909445, 11451034651712, 141307143171540, 1721381619036321, 20738815798941668, 247471563012643095, 2928344313826748362

Offset: 1

R. H. Hardin, Dec 06 2016

nonn

Column 7 of A279134.

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

R. H. Hardin, Table of n, a(n) for n = 1..83

Cf. A279134.

cp's OEIS Frontend

A279128 Number of n X 2 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279129 Number of nX3 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279130 Number of nX4 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279131 Number of nX5 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279132 Number of nX6 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279133 Number of nX7 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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Comments

Examples

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Crossrefs