A281051 Number of n X 3 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 6, 68, 376, 1492, 4988, 15028, 42252, 113076, 291660, 731060, 1791052, 4306868, 10197068, 23828404, 55060556, 125999028, 285894732, 643864500, 1440442444, 3203438516, 7086237772, 15599703988, 34190878796, 74638727092, 162339448908

Offset: 1

Author

R. H. Hardin, Jan 13 2017

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 3 of A281056.

Formula

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

Empirical g.f.: 2*x^2*(3 + x)*(1 + 2*x)*(1 + 4*x + 2*x^2) / ((1 + x)*(1 - 2*x)^3). - Colin Barker, Feb 15 2019