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A268633
Number of n X 2 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.
2
3, 24, 120, 504, 1944, 7128, 25272, 87480, 297432, 997272, 3306744, 10865016, 35429400, 114791256, 369882936, 1186176312, 3788111448, 12053081880, 38225488248, 120875192568, 381221761176, 1199453833944, 3765727153080
OFFSET
1,1
COMMENTS
Column 2 of A268639.
LINKS
FORMULA
Empirical: a(n) = 6*a(n-1) - 9*a(n-2) for n>3.
Conjectures from Colin Barker, Mar 21 2018: (Start)
G.f.: 3*x*(1 + x)^2 / (1 - 3*x)^2.
a(n) = 8*3^(n-2)*(2*n-1) for n>1.
(End)
EXAMPLE
Some solutions for n=8:
..0..1. .1..2. .2..1. .1..2. .2..2. .0..0. .0..0. .2..2. .1..2. .1..2
..1..0. .2..1. .1..0. .2..2. .1..2. .0..0. .0..0. .2..1. .2..1. .2..1
..2..1. .1..0. .2..1. .2..1. .2..1. .0..1. .0..0. .2..1. .2..2. .2..1
..2..1. .0..0. .1..0. .0..0. .2..2. .1..2. .1..0. .1..2. .1..2. .2..2
..2..2. .0..0. .2..2. .1..0. .2..2. .0..1. .0..1. .2..2. .0..0. .1..2
..2..1. .0..0. .2..2. .0..1. .0..1. .0..0. .1..0. .2..2. .1..0. .2..1
..1..0. .1..2. .2..2. .0..0. .0..0. .2..1. .2..2. .2..1. .0..0. .2..2
..0..0. .0..1. .2..2. .0..0. .0..0. .2..2. .2..2. .1..2. .0..1. .2..2
CROSSREFS
Cf. A268639.
Sequence in context: A127520 A175115 A301812 * A324065 A151883 A009134
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 09 2016
STATUS
approved