A280435 Number of nX3 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

1, 10, 21, 42, 77, 136, 236, 404, 687, 1162, 1959, 3294, 5528, 9262, 15497, 25898, 43233, 72100, 120132, 199992, 332675, 552970, 918491, 1524602, 2529072, 4192786, 6946941, 11503914, 19040117, 31497472, 52080284, 86073884, 142192983

Offset: 1

Author

R. H. Hardin, Jan 03 2017

Keywords

• nonn

Comments

Column 3 of A280440.

Examples

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

Links

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

Crossrefs

Cf. A280440.

Formula

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

Empirical g.f.: x -x^2*(10-9*x-11*x^2+2*x^3) / ( (x-1)*(x^2+x-1)^2 ). - R. J. Mathar, Jan 04 2017