A280233 -id:A280233 - cp's OEIS frontend

A280227 Number of n X 2 0..1 arrays with no element unequal 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, 4, 6, 8, 14, 24, 42, 72, 124, 212, 362, 616, 1046, 1772, 2996, 5056, 8518, 14328, 24066, 40368, 67628, 113164, 189154, 315848, 526894, 878164, 1462372, 2433272, 4045694, 6721752, 11160282, 18517656, 30706396, 50888132, 84287066, 139531816

Offset: 1

R. H. Hardin, Dec 29 2016

nonn

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

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

Column 2 of A280233.

Empirical: a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4) for n>7.

Empirical g.f.: x^2*(1 - x)*(1 + x)*(2 - x - 2*x^2 - x^3) / (1 - x - x^2)^2. - Colin Barker, Feb 13 2019

A280228 Number of n X 3 0..1 arrays with no element unequal 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, 6, 9, 16, 29, 52, 95, 168, 298, 522, 911, 1580, 2729, 4694, 8046, 13748, 23425, 39812, 67507, 114228, 192914, 325230, 547411, 919996, 1544029, 2588002, 4332630, 7245208, 12103013, 20197972, 33675911, 56098560, 93374074, 155296914

Offset: 1

R. H. Hardin, Dec 29 2016

nonn

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

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

Column 3 of A280233.

Empirical: a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4) for n>7.

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

A280229 Number of nX4 0..1 arrays with no element unequal 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, 8, 16, 48, 116, 288, 678, 1600, 3766, 8704, 20040, 45904, 104540, 237268, 536526, 1209480, 2719500, 6099968, 13653798, 30504064, 68032030, 151493220, 336863254, 748075672, 1659257392, 3676182044, 8136355808, 17990500384, 39743338382

Offset: 1

R. H. Hardin, Dec 29 2016

nonn

Column 4 of A280233.

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

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

Cf. A280233.

Empirical: a(n) = 4*a(n-1) -10*a(n-3) -8*a(n-4) +14*a(n-5) +25*a(n-6) +6*a(n-7) -10*a(n-8) -30*a(n-9) -27*a(n-10) -10*a(n-11) +9*a(n-12) +10*a(n-13) +3*a(n-14) +4*a(n-15) -4*a(n-16) for n>19

A280230 Number of nX5 0..1 arrays with no element unequal 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, 14, 29, 116, 355, 1102, 3376, 9860, 29091, 84644, 244759, 704628, 2018512, 5761462, 16393387, 46508232, 131619423, 371638678, 1047214662, 2945399940, 8270156835, 23184841888, 64903418567, 181446963548, 506630797962

Offset: 1

R. H. Hardin, Dec 29 2016

nonn

Column 5 of A280233.

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

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

Cf. A280233.

Empirical: a(n) = 4*a(n-1) +6*a(n-2) -28*a(n-3) -31*a(n-4) +78*a(n-5) +114*a(n-6) -90*a(n-7) -153*a(n-8) +66*a(n-9) -29*a(n-10) -246*a(n-11) +40*a(n-12) +278*a(n-13) -56*a(n-14) -114*a(n-15) +170*a(n-16) -24*a(n-17) -116*a(n-18) +40*a(n-19) +16*a(n-20) -4*a(n-21) -a(n-22) for n>25

A280231 Number of nX6 0..1 arrays with no element unequal 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, 24, 52, 288, 1102, 4260, 16282, 59648, 220330, 806580, 2928596, 10606308, 38210998, 137282336, 491839132, 1757295568, 6265155736, 22290508020, 79158223310, 280632840576, 993329469088, 3510893492340, 12392392661846

Offset: 1

R. H. Hardin, Dec 29 2016

nonn

Column 6 of A280233.

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

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

Cf. A280233.

A280232 Number of nX7 0..1 arrays with no element unequal 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, 42, 95, 678, 3376, 16282, 80825, 377706, 1780344, 8321484, 38431266, 177322266, 812861536, 3712259660, 16906747879, 76738963064, 347459922194, 1569637145558, 7075367986446, 31833804360316, 142976818494750, 641124031114626

Offset: 1

R. H. Hardin, Dec 29 2016

nonn

Column 7 of A280233.

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

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

Cf. A280233.

cp's OEIS Frontend

A280227 Number of n X 2 0..1 arrays with no element unequal 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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A280228 Number of n X 3 0..1 arrays with no element unequal 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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A280229 Number of nX4 0..1 arrays with no element unequal 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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A280230 Number of nX5 0..1 arrays with no element unequal 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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A280231 Number of nX6 0..1 arrays with no element unequal 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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A280232 Number of nX7 0..1 arrays with no element unequal 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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