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A188819 Number of n X 3 binary arrays without the pattern 0 1 diagonally or antidiagonally. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A161448 A031096 A303194 * A123605 A273743 A089613

Adjacent sequences: A188816 A188817 A188818 * A188820 A188821 A188822

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 11 2011

STATUS

approved

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Last modified December 8 12:03 EST 2022. Contains 358693 sequences. (Running on oeis4.)