A279152 Number of n X 2 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 4, 12, 30, 72, 162, 356, 766, 1616, 3378, 7004, 14406, 29480, 60090, 122036, 247150, 499456, 1007458, 2029068, 4081686, 8202456, 16469642, 33046628, 66271166, 132836784, 266160818, 533127612, 1067587174, 2137374088, 4278378970

Offset: 1

Author

R. H. Hardin, Dec 06 2016

Keywords

• nonn

Examples

			Some solutions for n=4:
..0..1. .0..1. .0..1. .0..1. .0..0. .0..0. .0..0. .0..1. .0..0. .0..0
..1..1. .1..0. .0..1. .0..1. .1..1. .1..1. .1..1. .1..0. .1..1. .1..1
..0..0. .0..0. .1..1. .0..0. .1..0. .0..0. .0..1. .1..1. .0..1. .1..0
..1..1. .1..1. .0..0. .1..1. .0..1. .1..0. .1..0. .0..0. .0..1. .1..0
		

Links

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

Crossrefs

Column 2 of A279158.

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 6*a(n-3) - 12*a(n-4) + 8*a(n-5) - 4*a(n-6) + 8*a(n-7).

Empirical g.f.: 2*x^3*(2 - 2*x + x^2 - 6*x^3) / ((1 - 2*x)*(1 - x - 2*x^3)^2). - Colin Barker, Feb 10 2019