A279162 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 two elements, and with new values introduced in order 0 sequentially upwards.

1, 0, 0, 8, 24, 88, 284, 772, 2000, 5008, 12060, 28300, 65192, 147736, 330340, 730740, 1601744, 3483616, 7526252, 16167132, 34555192, 73534440, 155880628, 329312132, 693584736, 1456820784, 3052436156, 6381514348, 13314563144, 27728987832

Offset: 1

Author

R. H. Hardin, Dec 07 2016

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 2 of A279168.

Formula

Empirical: a(n) = 7*a(n-1) - 19*a(n-2) + 31*a(n-3) - 52*a(n-4) + 82*a(n-5) - 84*a(n-6) + 84*a(n-7) - 96*a(n-8) + 56*a(n-9) - 32*a(n-10) + 32*a(n-11).

Empirical g.f.: x*(1 - 7*x + 19*x^2 - 23*x^3 + 20*x^4 - 10*x^5 - 40*x^6 + 44*x^7 - 48*x^8 + 96*x^9) / ((1 - 2*x)^2*(1 - x - 2*x^3)^3). - Colin Barker, Feb 10 2019