A280174 Number of n X 2 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

1, 2, 12, 41, 103, 263, 656, 1618, 3931, 9459, 22557, 53395, 125594, 293796, 683972, 1585588, 3661900, 8428646, 19341455, 44261305, 101034472, 230100558, 522936849, 1186138105, 2685582035, 6070360107, 13699764020, 30873005212, 69478759648

Offset: 1

Author

R. H. Hardin, Dec 28 2016

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 2 of A280180.

Formula

Empirical: a(n) = 4*a(n-1) - 11*a(n-3) - 4*a(n-4) + 15*a(n-5) + 14*a(n-6) - 2*a(n-7) - 9*a(n-8) - 5*a(n-9) - a(n-10) for n>14.

Empirical g.f.: x*(1 - 2*x + 4*x^2 + 4*x^3 - 35*x^4 - 24*x^5 + 59*x^6 + 85*x^7 - 6*x^8 - 69*x^9 - 43*x^10 - 5*x^11 + 3*x^12 + x^13) / ((1 - x)*(1 - x - 2*x^2 - x^3)^3). - Colin Barker, Feb 13 2019