A279158 -id:A279158 - cp's OEIS frontend

A279152 Number of n X 2 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 4, 12, 30, 72, 162, 356, 766, 1616, 3378, 7004, 14406, 29480, 60090, 122036, 247150, 499456, 1007458, 2029068, 4081686, 8202456, 16469642, 33046628, 66271166, 132836784, 266160818, 533127612, 1067587174, 2137374088, 4278378970

Offset: 1

R. H. Hardin, Dec 06 2016

nonn

			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
..1..1. .1..0. .0..1. .0..1. .1..1. .1..1. .1..1. .1..0. .1..1. .1..1
..0..0. .0..0. .1..1. .0..0. .1..0. .0..0. .0..1. .1..1. .0..1. .1..0
..1..1. .1..1. .0..0. .1..1. .0..1. .1..0. .1..0. .0..0. .0..1. .1..0

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

Column 2 of A279158.

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 6*a(n-3) - 12*a(n-4) + 8*a(n-5) - 4*a(n-6) + 8*a(n-7).

Empirical g.f.: 2*x^3*(2 - 2*x + x^2 - 6*x^3) / ((1 - 2*x)*(1 - x - 2*x^3)^2). - Colin Barker, Feb 10 2019

A279153 Number of nX3 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

2, 4, 20, 72, 255, 874, 2903, 9336, 29578, 92528, 285992, 875912, 2662819, 8042606, 24156735, 72211820, 214959872, 637526372, 1884571600, 5554575752, 16328272725, 47884030342, 140118979793, 409205295972, 1192876666588, 3471548282192

Offset: 1

R. H. Hardin, Dec 06 2016

nonn

Column 3 of A279158.

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

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

Cf. A279158.

Empirical: a(n) = 8*a(n-1) -24*a(n-2) +44*a(n-3) -90*a(n-4) +158*a(n-5) -168*a(n-6) +208*a(n-7) -261*a(n-8) +128*a(n-9) -149*a(n-10) +188*a(n-11) -12*a(n-12) +162*a(n-13) -130*a(n-14) -56*a(n-15) -80*a(n-16) +31*a(n-18) +56*a(n-19) +4*a(n-20) -16*a(n-21) -4*a(n-22) for n>23

A279154 Number of nX4 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

2, 12, 72, 428, 2294, 11932, 60304, 297092, 1443498, 6930508, 32917852, 155025096, 724982468, 3370079700, 15584464186, 71742003424, 328950577598, 1503015006696, 6845967619642, 31094637435220, 140875688981220, 636779907204164

Offset: 1

R. H. Hardin, Dec 06 2016

nonn

Column 4 of A279158.

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

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

Cf. A279158.

Empirical: a(n) = 14*a(n-1) -79*a(n-2) +296*a(n-3) -1137*a(n-4) +3786*a(n-5) -9491*a(n-6) +25574*a(n-7) -66007*a(n-8) +125068*a(n-9) -286655*a(n-10) +644352*a(n-11) -935651*a(n-12) +2106274*a(n-13) -4254326*a(n-14) +4407958*a(n-15) -11660139*a(n-16) +20200812*a(n-17) -12942101*a(n-18) +52398124*a(n-19) -69889240*a(n-20) +21188756*a(n-21) -190043003*a(n-22) +177570770*a(n-23) -9931732*a(n-24) +525736690*a(n-25) -354049840*a(n-26) -26853854*a(n-27) -1062956470*a(n-28) +606320574*a(n-29) +18947687*a(n-30) +1546195654*a(n-31) -882316499*a(n-32) +192000088*a(n-33) -1655999570*a(n-34) +946806094*a(n-35) -559625950*a(n-36) +1454800834*a(n-37) -725310313*a(n-38) +650909536*a(n-39) -1073036990*a(n-40) +514311888*a(n-41) -448474953*a(n-42) +540383844*a(n-43) -298642984*a(n-44) +247525328*a(n-45) -191218312*a(n-46) +91813964*a(n-47) -69588676*a(n-48) +52628912*a(n-49) -21603676*a(n-50) +3806952*a(n-51) -2143540*a(n-52) +961488*a(n-53) -183280*a(n-54) -15808*a(n-55) -23104*a(n-56) for n>57

A279155 Number of n X 5 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

5, 30, 255, 2294, 20104, 166552, 1331471, 10508084, 81594334, 624717186, 4739157622, 35661603332, 266406928267, 1978392492492, 14617489508922, 107516403089962, 787701900591720, 5750928990829306, 41856485102494388

Offset: 1

R. H. Hardin, Dec 06 2016

nonn

Column 5 of A279158.

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

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

Cf. A279158.

A279156 Number of nX6 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

8, 72, 874, 11932, 166552, 2145788, 26724386, 330704288, 4027185426, 48341053840, 575447444416, 6798252425856, 79744778501470, 930090029926488, 10795234169830306, 124750828432766768, 1436120215880230752

Offset: 1

R. H. Hardin, Dec 06 2016

nonn

Column 6 of A279158.

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

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

Cf. A279158.

A279157 Number of nX7 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

15, 162, 2903, 60304, 1331471, 26724386, 517476726, 10025433990, 191191601644, 3592564336954, 66997045991457, 1240581415395934, 22812879393607545, 417195888212408920, 7594010221332762302, 137646990170206088748

Offset: 1

R. H. Hardin, Dec 06 2016

nonn

Column 7 of A279158.

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

R. H. Hardin, Table of n, a(n) for n = 1..100

Cf. A279158.

cp's OEIS Frontend

A279152 Number of n X 2 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279153 Number of nX3 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279154 Number of nX4 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279155 Number of n X 5 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279156 Number of nX6 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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A279157 Number of nX7 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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Examples

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