A188819 Number of n X 3 binary arrays without the pattern 0 1 diagonally or antidiagonally.

8, 25, 48, 81, 120, 169, 224, 289, 360, 441, 528, 625, 728, 841, 960, 1089, 1224, 1369, 1520, 1681, 1848, 2025, 2208, 2401, 2600, 2809, 3024, 3249, 3480, 3721, 3968, 4225, 4488, 4761, 5040, 5329, 5624, 5929, 6240, 6561, 6888, 7225, 7568, 7921, 8280, 8649

Offset: 1

Author

R. H. Hardin, Apr 11 2011

Keywords

• nonn

Comments

Column 3 of A188824.

Examples

			Some solutions for 4 X 3:
..1..1..1....1..1..1....1..1..0....1..1..1....1..0..1....0..1..0....0..1..0
..0..1..1....1..1..1....1..0..1....1..1..1....0..0..0....1..0..1....1..0..1
..1..0..1....1..0..0....0..1..0....1..1..1....0..0..0....0..0..0....0..1..0
..0..0..0....0..0..0....0..0..1....1..1..1....0..0..0....0..0..0....1..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A188824.

Formula

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).

Conjectures from Colin Barker, Apr 29 2018: (Start)

G.f.: x*(8 + 9*x - 2*x^2 + x^3) / ((1 - x)^3*(1 + x)).

a(n) = (2 + 8*n + 8*n^2) / 2 for n even.

a(n) = (8*n + 8*n^2) / 2 for n odd.

(End)