A188865 Number of n X 8 binary arrays without the pattern 0 1 diagonally, vertically or antidiagonally.

256, 1393, 3194, 5275, 7442, 9627, 11814, 14001, 16188, 18375, 20562, 22749, 24936, 27123, 29310, 31497, 33684, 35871, 38058, 40245, 42432, 44619, 46806, 48993, 51180, 53367, 55554, 57741, 59928, 62115, 64302, 66489, 68676, 70863, 73050, 75237, 77424

Offset

1,1

Comments

Column 8 of A188866.

Links

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

Formula

Empirical: a(n) = 2187*n - 3495 for n>5.

Conjectures from Colin Barker, Feb 28 2018: (Start)

G.f.: x*(256 + 881*x + 664*x^2 + 280*x^3 + 86*x^4 + 18*x^5 + 2*x^6) / (1 - x)^2.

a(n) = 2*a(n-1) - a(n-2) for n>7.

(End)

Example

Some solutions for 3 X 8:
..1..1..1..1..1..1..1..1....1..1..1..1..1..1..1..1....1..1..0..1..1..1..1..1
..1..1..1..1..1..1..1..1....1..1..1..1..1..1..1..1....0..0..0..0..1..1..1..1
..0..0..0..0..1..1..1..0....0..0..1..0..1..1..1..0....0..0..0..0..0..0..0..0

Crossrefs

Cf. A188866.

Sequence in context: A206320 A237315 A237309 * A187964 A187956 A237225

Adjacent sequences: A188862 A188863 A188864 * A188866 A188867 A188868

Keyword

nonn

Author

R. H. Hardin, Apr 12 2011

Status

approved