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

0,2

Comments

Diagonal of A188866.

Links

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

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

Example

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

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

Crossrefs

Cf. A188866.

Sequence in context: A134063 A087448 A289449 * A129273 A055988 A371798

Adjacent sequences: A188857 A188858 A188859 * A188861 A188862 A188863

Keyword

nonn

Author

R. H. Hardin, Apr 12 2011

Extensions

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

Status

approved