A188860 Number of n X n binary arrays without the pattern 0 1 diagonally, vertically or antidiagonally.

1, 2, 7, 26, 95, 340, 1193, 4116, 14001, 47064, 156629, 516844, 1693073, 5511218, 17841247, 57477542, 184377699, 589195584, 1876395357, 5957318820, 18861068265, 59563612974, 187668462027, 590039959434, 1851508693479, 5799494052414, 18135645594003

Offset: 0

Author

R. H. Hardin, Apr 12 2011

Keywords

• nonn

Comments

Diagonal of A188866.

Examples

			Some solutions for 3X3
..1..1..1....0..0..0....1..1..1....1..1..1....1..1..0....1..1..1....1..1..1
..1..1..1....0..0..0....1..1..1....1..0..0....0..0..0....1..1..1....1..1..1
..1..1..0....0..0..0....1..0..0....0..0..0....0..0..0....1..0..1....0..0..0
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000 (terms n = 1..32 from R. H. Hardin)

Crossrefs

Cf. A188866.

Programs

Maple

a:= proc(n) option remember; `if`(n<3, (2*n-1)*n+1,
      ((10*n^2-49*n+33)*a(n-1)-(6*n^2-9*n-33)*a(n-2)
       -(9*(n-3))*(2*n-7)*a(n-3))/((n-1)*(2*n-9)))
    end:
seq(a(n), n=0..35);  # Alois P. Heinz, Mar 30 2017

Formula

G.f.: (3*x^2-3*x+1-x*sqrt(1-3*x^2-2*x))/(1-3*x)^2. - Alois P. Heinz, Mar 30 2017

Extensions

a(0)=1 prepended by Alois P. Heinz, Mar 30 2017