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.

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

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

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: 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