A188841 Number of n X 7 binary arrays without the pattern 0 1 diagonally or vertically.

128, 987, 3280, 7753, 15504, 28101, 47652, 76912, 119416, 179630, 263120, 376740, 528840, 729495, 990756, 1326924, 1754848, 2294248, 2968064, 3802832, 4829088, 6081801, 7600836, 9431448, 11624808, 14238562, 17337424, 20993804, 25288472

Offset: 1

Author

R. H. Hardin, Apr 12 2011

Keywords

• nonn

Comments

Column 7 of A188843.

Examples

			Some solutions for 3 X 7:
..1..1..0..0..1..1..1....1..1..1..1..1..1..1....1..0..0..1..1..0..0
..1..1..0..0..0..1..1....1..1..0..1..1..1..1....1..0..0..0..1..0..0
..1..1..0..0..0..0..0....0..0..0..0..0..0..0....1..0..0..0..0..0..0
		

Links

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

Crossrefs

Cf. A188843.

Formula

Empirical: a(n) = (1/5040)*n^7 + (1/72)*n^6 + (143/360)*n^5 + (53/9)*n^4 + (33667/720)*n^3 + (12679/72)*n^2 + (9439/70)*n - 572 for n>4.

Empirical g.f.: x*(128 - 37*x - 1032*x^2 + 1981*x^3 - 992*x^4 - 605*x^5 + 700*x^6 - 58*x^7 - 96*x^8 + 3*x^9 + 8*x^10 + x^11) / (1 - x)^8. - Colin Barker, May 01 2018