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A269146
Number of n X 2 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.
1
4, 80, 768, 6224, 46464, 330192, 2270592, 15251152, 100647168, 655139152, 4217820672, 26911075152, 170416738944, 1072338720464, 6710943646848, 41800542176720, 259288295447040, 1602497927690832, 9871915467776256
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 12*a(n-1) - 38*a(n-2) + 12*a(n-3) - a(n-4) for n>5.
Empirical g.f.: 4*x*(1 - x)*(1 + 9*x - x^2 - x^3) / (1 - 6*x + x^2)^2. - Colin Barker, Jan 19 2019
EXAMPLE
Some solutions for n=4:
..3..2. .0..0. .2..0. .3..3. .1..0. .1..0. .1..3. .3..1. .0..2. .1..1
..2..0. .2..3. .0..2. .3..3. .1..1. .0..2. .0..1. .1..0. .0..0. .3..3
..1..0. .2..2. .0..3. .1..0. .1..3. .0..0. .0..0. .0..1. .2..3. .3..2
..0..1. .3..3. .2..3. .0..0. .1..0. .1..3. .2..0. .0..2. .3..3. .0..2
CROSSREFS
Column 2 of A269152.
Sequence in context: A093854 A345459 A366955 * A192834 A054322 A114488
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 20 2016
STATUS
approved