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A268622
Number of n X 2 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.
2
9, 42, 174, 666, 2430, 8586, 29646, 100602, 336798, 1115370, 3661038, 11927898, 38618046, 124357194, 398580750, 1272269754, 4046391774, 12827922858, 40550011182, 127848761370, 402142467582, 1262215953162, 3954013510734
OFFSET
1,1
COMMENTS
Column 2 of A268628.
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*(3 - x)*(1 - x) / (1 - 3*x)^2.
a(n) = 2*3^(n-2)*(5+8*n) for n>1.
(End)
EXAMPLE
Some solutions for n=8:
..1..0. .0..1. .2..1. .1..2. .2..2. .0..1. .0..0. .0..0. .1..0. .1..0
..2..2. .1..0. .1..0. .2..1. .2..2. .1..0. .0..1. .0..1. .2..2. .0..0
..2..1. .2..1. .2..1. .1..2. .1..2. .2..1. .0..0. .0..0. .1..2. .1..2
..2..2. .2..2. .1..0. .2..2. .2..2. .2..2. .1..0. .0..0. .0..1. .2..1
..2..1. .1..2. .2..1. .2..2. .2..1. .2..1. .0..1. .0..0. .1..0. .1..2
..2..2. .2..2. .1..2. .2..1. .2..2. .2..0. .0..0. .1..0. .2..1. .2..2
..1..2. .1..2. .1..2. .1..2. .0..1. .1..0. .1..0. .2..2. .2..2. .1..2
..2..2. .0..0. .0..1. .2..1. .1..2. .0..0. .0..1. .1..2. .1..2. .0..1
CROSSREFS
Cf. A268628.
Sequence in context: A268262 A293101 A084899 * A289364 A074443 A221425
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 09 2016
STATUS
approved