A188822 Number of n X 7 binary arrays without the pattern 0 1 diagonally or antidiagonally.

128, 1156, 3888, 8836, 15776, 24964, 36000, 49284, 64416, 81796, 101024, 122500, 145824, 171396, 198816, 228484, 260000, 293764, 329376, 367236, 406944, 448900, 492704, 538756, 586656, 636804, 688800, 743044, 799136, 857476, 917664, 980100

Offset: 1

Author

R. H. Hardin, Apr 11 2011

Keywords

• nonn

Comments

Column 7 of A188824.

Examples

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

Links

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

Crossrefs

Cf. A188824.

Formula

Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>7.

Conjectures from Colin Barker, Apr 30 2018: (Start)

G.f.: 4*x*(32 + 225*x + 394*x^2 + 329*x^3 + 72*x^4 + 8*x^5 - 36*x^6) / ((1 - x)^3*(1 + x)).

a(n) = 2*(578 - 1088*n + 512*n^2) for n>3 and even.

a(n) = 2*(528 - 1088*n + 512*n^2) for n>3 and odd.

(End)