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A268775
Number of n X 2 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two no more than once.
1
4, 11, 26, 65, 148, 343, 766, 1709, 3752, 8195, 17746, 38233, 81916, 174767, 371366, 786437, 1660240, 3495259, 7340026, 15379121, 32156324, 67108871, 139810126, 290805085, 603979768, 1252698803, 2594876066, 5368709129, 11095332172
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 4*a(n-4).
Conjectures from Colin Barker, Jan 15 2019: (Start)
G.f.: x*(4 + 3*x - 8*x^2 - 4*x^3) / ((1 + x)^2*(1 - 2*x)^2).
a(n) = ((-1)^(1+n) + 2^(2+n) + ((-1)^n+2^(1+n))*n) / 3.
(End)
EXAMPLE
Some solutions for n=4:
..0..0. .0..0. .0..1. .0..1. .1..0. .0..0. .0..0. .1..0. .1..1. .0..0
..0..0. .1..1. .1..0. .0..0. .0..0. .1..1. .0..0. .0..0. .0..0. .0..1
..0..1. .0..0. .0..0. .1..1. .0..0. .0..0. .1..0. .0..1. .0..1. .0..0
..1..0. .1..0. .1..0. .0..0. .1..0. .0..1. .1..0. .1..0. .0..0. .1..0
CROSSREFS
Column 2 of A268781.
Sequence in context: A373358 A183276 A340567 * A294840 A014630 A192965
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 13 2016
STATUS
approved