A281832 Number of n X 3 0..1 arrays with no element equal to more than four of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

4, 31, 163, 926, 5315, 30387, 174121, 998069, 5720443, 32788987, 187945010, 1077290419, 6174981492, 35394734997, 202881130985, 1162906171769, 6665729691190, 38207684670140, 219004855904382, 1255326705617567

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) + 4*a(n-2) + 6*a(n-3) - 23*a(n-4) - 25*a(n-5) - 15*a(n-6) - 28*a(n-7) for n>8.

Empirical g.f.: x*(4 + 11*x - 8*x^2 - 37*x^3 - 61*x^4 - 57*x^5 - 46*x^6 - 24*x^7) / (1 - 5*x - 4*x^2 - 6*x^3 + 23*x^4 + 25*x^5 + 15*x^6 + 28*x^7). - Colin Barker, Feb 20 2019

Example

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

Crossrefs

Column 3 of A281837.

Sequence in context: A263762 A263763 A179562 * A299076 A270670 A270669

Adjacent sequences: A281829 A281830 A281831 * A281833 A281834 A281835

Keyword

nonn

Author

R. H. Hardin, Jan 31 2017

Status

approved