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A268965
Number of n X 2 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.
1
9, 60, 336, 1728, 8448, 39936, 184320, 835584, 3735552, 16515072, 72351744, 314572800, 1358954496, 5838471168, 24964497408, 106300440576, 450971566080, 1906965479424, 8040178778112, 33809982554112, 141836999983104
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 8*a(n-1) - 16*a(n-2).
Conjectures from Colin Barker, Jan 17 2019: (Start)
G.f.: 3*x*(3 - 4*x) / (1 - 4*x)^2.
a(n) = 4^(n-1) * (6*n+3).
(End)
EXAMPLE
Some solutions for n=4:
..0..0. .0..0. .0..1. .2..2. .1..2. .1..0. .2..2. .0..2. .2..1. .0..1
..0..2. .1..1. .0..0. .1..1. .2..0. .0..0. .2..1. .2..1. .0..2. .2..2
..2..2. .2..1. .2..2. .2..2. .0..1. .2..2. .2..1. .0..0. .1..2. .2..0
..1..0. .2..1. .2..2. .2..1. .2..1. .1..0. .2..2. .0..0. .2..2. .1..2
CROSSREFS
Column 2 of A268971.
Sequence in context: A268972 A288962 A074431 * A081904 A085373 A241976
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 16 2016
STATUS
approved