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A283488
Number of n X 2 0..1 arrays with no 1 equal to more than three of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element.
1
0, 0, 2, 12, 64, 312, 1460, 6624, 29394, 128264, 552384, 2353888, 9943896, 41703328, 173822258, 720671156, 2974187392, 12224902712, 50069348140, 204417445696, 832198630882, 3379257614032, 13690075484800, 55344113101440
OFFSET
1,3
LINKS
FORMULA
Empirical: a(n) = 6*a(n-1) - 3*a(n-2) - 16*a(n-3) - 13*a(n-4) - 10*a(n-5) - 13*a(n-6) - 8*a(n-7) - 3*a(n-8) - 2*a(n-9) - a(n-10).
Empirical g.f.: 2*x^3*(1 - x - x^2)*(1 + x + x^2) / (1 - 3*x - 3*x^2 - x^3 - x^4 - x^5)^2. - Colin Barker, Feb 21 2019
EXAMPLE
Some solutions for n=4:
..0..1. .0..1. .1..1. .1..0. .1..1. .0..0. .0..1. .1..1. .1..1. .0..0
..1..1. .1..1. .1..1. .1..1. .1..1. .0..1. .0..1. .1..1. .1..1. .1..1
..1..1. .1..1. .1..0. .1..1. .1..0. .1..1. .1..1. .1..0. .1..0. .1..1
..0..0. .0..1. .1..1. .1..0. .0..1. .1..1. .1..1. .0..0. .1..0. .1..0
CROSSREFS
Column 2 of A283494.
Sequence in context: A330387 A368760 A272363 * A006646 A087635 A180038
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 08 2017
STATUS
approved