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A280155
Number of n X 2 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
1
0, 4, 8, 18, 40, 92, 208, 470, 1060, 2384, 5352, 11992, 26824, 59906, 133592, 297510, 661720, 1470062, 3262264, 7231940, 16016596, 35439722, 78349800, 173074816, 382029988, 842648168, 1857362384, 4091321478, 9006604780, 19815365450
OFFSET
1,2
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 2*a(n-3) - 6*a(n-4) - 4*a(n-5) - a(n-6) for n>8.
Empirical g.f.: 2*x^2*(2 - 5*x^2 - 6*x^3 - x^4 + 2*x^5 + x^6) / (1 - x - 2*x^2 - x^3)^2. - Colin Barker, Feb 13 2019
EXAMPLE
Some solutions for n=4:
..0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..1
..0..0. .0..0. .0..1. .0..0. .0..1. .1..0. .0..0. .0..1. .1..1. .0..0
..1..1. .1..0. .1..1. .0..0. .0..0. .0..0. .0..0. .1..1. .1..0. .0..1
..1..0. .0..0. .0..0. .0..1. .0..0. .0..0. .1..1. .1..0. .0..0. .1..1
CROSSREFS
Column 2 of A280161.
Sequence in context: A228231 A175657 A080287 * A075310 A075797 A351323
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 27 2016
STATUS
approved