A279168 -id:A279168 - cp's OEIS frontend

A279162 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 two elements, and with new values introduced in order 0 sequentially upwards.

1, 0, 0, 8, 24, 88, 284, 772, 2000, 5008, 12060, 28300, 65192, 147736, 330340, 730740, 1601744, 3483616, 7526252, 16167132, 34555192, 73534440, 155880628, 329312132, 693584736, 1456820784, 3052436156, 6381514348, 13314563144, 27728987832

Offset: 1

R. H. Hardin, Dec 07 2016

nonn

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

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

Column 2 of A279168.

Empirical: a(n) = 7*a(n-1) - 19*a(n-2) + 31*a(n-3) - 52*a(n-4) + 82*a(n-5) - 84*a(n-6) + 84*a(n-7) - 96*a(n-8) + 56*a(n-9) - 32*a(n-10) + 32*a(n-11).

Empirical g.f.: x*(1 - 7*x + 19*x^2 - 23*x^3 + 20*x^4 - 10*x^5 - 40*x^6 + 44*x^7 - 48*x^8 + 96*x^9) / ((1 - 2*x)^2*(1 - x - 2*x^3)^3). - Colin Barker, Feb 10 2019

A279163 Number of nX3 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 0, 16, 117, 483, 2001, 7709, 28139, 99519, 343156, 1158512, 3846322, 12594188, 40751991, 130532891, 414450312, 1305793262, 4086143226, 12709088120, 39314219923, 121018445801, 370868139707, 1131946765331, 3442082089719

Offset: 1

R. H. Hardin, Dec 07 2016

nonn

Column 3 of A279168.

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

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

Cf. A279168.

Empirical: a(n) = 12*a(n-1) -60*a(n-2) +178*a(n-3) -423*a(n-4) +945*a(n-5) -1762*a(n-6) +2718*a(n-7) -4107*a(n-8) +5541*a(n-9) -6003*a(n-10) +6900*a(n-11) -7369*a(n-12) +5673*a(n-13) -6435*a(n-14) +6357*a(n-15) -3486*a(n-16) +5577*a(n-17) -3953*a(n-18) +453*a(n-19) -3432*a(n-20) +780*a(n-21) +357*a(n-22) +2541*a(n-23) +430*a(n-24) -354*a(n-25) -888*a(n-26) -583*a(n-27) -84*a(n-28) +354*a(n-29) +224*a(n-30) -36*a(n-31) -48*a(n-32) -8*a(n-33) for n>36

A279164 Number of nX4 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

3, 8, 117, 864, 5628, 34764, 203226, 1143396, 6219491, 33013384, 171939641, 880916518, 4451397177, 22233587926, 109941169416, 538893155258, 2621198787932, 12662917887190, 60802741447447, 290361255593144

Offset: 1

R. H. Hardin, Dec 07 2016

nonn

Column 4 of A279168.

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

R. H. Hardin, Table of n, a(n) for n = 1..250
R. H. Hardin, Empirical recurrence of order 84

Cf. A279168.

Empirical recurrence of order 84 (see link above)

A279165 Number of nX5 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

3, 24, 483, 5628, 57248, 557163, 5159514, 45915548, 396958758, 3354431037, 27818139968, 227109345763, 1829793702631, 14577379224104, 115006531796224, 899624259907987, 6984552550608837, 53866857503363854, 412968368588533755

Offset: 1

R. H. Hardin, Dec 07 2016

nonn

Column 5 of A279168.

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

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

Cf. A279168.

A279166 Number of nX6 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

9, 88, 2001, 34764, 557163, 8426362, 121098448, 1686053298, 22825771952, 302051174586, 3926950483003, 50292947670984, 635850396680521, 7951563133669828, 98499861578102570, 1210045057467722370

Offset: 1

R. H. Hardin, Dec 07 2016

nonn

Column 6 of A279168.

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

R. H. Hardin, Table of n, a(n) for n = 1..145

Cf. A279168.

A279167 Number of nX7 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

15, 284, 7709, 203226, 5159514, 121098448, 2708250146, 58954576326, 1248383818884, 25842455526113, 526028318802380, 10553193022979559, 209056148689381340, 4097404879908777416, 79569078719501719249

Offset: 1

R. H. Hardin, Dec 07 2016

nonn

Column 7 of A279168.

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

R. H. Hardin, Table of n, a(n) for n = 1..55

Cf. A279168.

cp's OEIS Frontend

A279162 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 two elements, and with new values introduced in order 0 sequentially upwards.

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A279163 Number of nX3 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279164 Number of nX4 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279165 Number of nX5 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279166 Number of nX6 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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A279167 Number of nX7 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

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