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A269180
Number of n X 2 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.
1
4, 48, 384, 2736, 18336, 118032, 739008, 4533744, 27384288, 163381968, 965118720, 5654345136, 32898781728, 190290667152, 1095084877632, 6274151751024, 35807326610016, 203653219107408, 1154714957732736, 6529188836867376
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 10*a(n-1) - 21*a(n-2) - 20*a(n-3) - 4*a(n-4) for n>5.
Empirical g.f.: 4*x*(1 - x)^2*(1 + 2*x)^2 / (1 - 5*x - 2*x^2)^2. - Colin Barker, Jan 19 2019
EXAMPLE
Some solutions for n=4:
..1..1. .2..3. .3..3. .1..0. .3..0. .0..2. .1..1. .2..0. .1..0. .1..1
..0..0. .2..0. .1..3. .2..0. .2..2. .2..0. .1..3. .1..0. .0..0. .0..0
..2..0. .2..0. .0..1. .0..0. .2..0. .1..0. .1..3. .0..0. .1..0. .1..0
..3..2. .2..2. .0..1. .0..0. .2..0. .0..0. .1..0. .0..0. .3..1. .1..3
CROSSREFS
Column 2 of A269186.
Sequence in context: A091904 A192831 A158681 * A228701 A111903 A059409
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 20 2016
STATUS
approved