A208378 Number of n X 7 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

42, 1764, 6216, 13860, 25200, 40740, 60984, 86436, 117600, 154980, 199080, 250404, 309456, 376740, 452760, 538020, 633024, 738276, 854280, 981540, 1120560, 1271844, 1435896, 1613220, 1804320, 2009700, 2229864, 2465316, 2716560, 2984100, 3268440

Offset

1,1

Comments

Column 7 of A208379.

Links

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

Formula

Empirical: a(n) = 84*n^3 + 840*n^2 - 1344*n + 420 for n>1.

Conjectures from Colin Barker, Jul 02 2018: (Start)

G.f.: 42*x*(1 + 38*x - 14*x^2 - 14*x^3 + x^4) / (1 - x)^4.

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

(End)

Example

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

Crossrefs

Cf. A208379.

Sequence in context: A207588 A207844 A206986 * A208068 A207933 A207850

Adjacent sequences: A208375 A208376 A208377 * A208379 A208380 A208381

Keyword

nonn

Author

R. H. Hardin, Feb 25 2012

Status

approved