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

1,1

Comments

Column 3 of A188824.

Links

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

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)

Example

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

Crossrefs

Cf. A188824.

Sequence in context: A031096 A373892 A303194 * A123605 A273743 A089613

Adjacent sequences: A188816 A188817 A188818 * A188820 A188821 A188822

Keyword

nonn

Author

R. H. Hardin, Apr 11 2011

Status

approved