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

Author

R. H. Hardin, Apr 12 2011

Keywords

• nonn

Comments

Column 8 of A188866.

Examples

			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
		

Links

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

Crossrefs

Cf. A188866.

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)