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A279852
Number of n X 3 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
1
2, 10, 49, 168, 557, 1758, 5441, 16500, 49253, 145290, 424425, 1229824, 3539405, 10127350, 28832593, 81728396, 230776757, 649427170, 1821994809, 5097729560, 14227693853, 39620451150, 110107647905, 305424435364, 845754303493
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 9*a(n-4) - 4*a(n-5) - 4*a(n-6) for n>9.
Empirical g.f.: x*(2 + 2*x + 13*x^2 - 8*x^3 + x^4 - 36*x^5 + 12*x^6 + 16*x^8) / (1 - 2*x - x^2 - 2*x^3)^2. - Colin Barker, Feb 11 2019
EXAMPLE
Some solutions for n=4:
..0..0..0. .0..0..0. .0..1..1. .0..1..1. .0..0..0. .0..1..1. .0..0..1
..1..1..1. .1..1..1. .1..1..1. .0..1..1. .0..0..0. .0..1..1. .1..1..1
..1..1..1. .1..1..1. .1..1..1. .0..1..1. .1..0..0. .0..0..0. .1..1..1
..2..2..1. .1..0..1. .0..0..0. .0..0..1. .1..0..0. .0..2..0. .2..2..2
CROSSREFS
Column 3 of A279856.
Sequence in context: A270664 A330543 A052576 * A219662 A355153 A268108
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 20 2016
STATUS
approved