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A268899
Number of n X 3 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.
1
12, 168, 1584, 12960, 98496, 715392, 5038848, 34712064, 235146240, 1572120576, 10400182272, 68205846528, 444063596544, 2873352683520, 18493942726656, 118486616113152, 756057455198208, 4807171282305024, 30467987000524800
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 12*a(n-1) - 36*a(n-2).
Conjectures from Colin Barker, Jan 16 2019: (Start)
G.f.: 12*x*(1 + 2*x) / (1 - 6*x)^2.
a(n) = 2^(n+1) * 3^(n-1) * (4*n-1).
(End)
EXAMPLE
Some solutions for n=4:
..2..1..1. .1..0..1. .2..2..2. .0..1..0. .0..0..0. .1..0..2. .0..0..0
..0..0..0. .0..2..2. .1..1..0. .2..1..0. .0..0..1. .0..1..0. .1..2..1
..0..0..0. .1..2..1. .2..1..2. .1..0..1. .1..0..2. .0..1..2. .1..0..1
..0..0..0. .2..2..2. .2..2..2. .1..0..1. .0..1..0. .2..1..0. .1..0..1
CROSSREFS
Column 3 of A268904.
Sequence in context: A324414 A099745 A360352 * A366710 A182606 A079679
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 15 2016
STATUS
approved