

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
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OFFSET

1,1


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210


FORMULA

Empirical: a(n) = 2*a(n1) + 3*a(n2)  4*a(n3)  4*a(n4).
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: A036891 A183276 A340567 * A294840 A014630 A192965
Adjacent sequences: A268772 A268773 A268774 * A268776 A268777 A268778


KEYWORD

nonn


AUTHOR

R. H. Hardin, Feb 13 2016


STATUS

approved



