A202194 Number of (n+2)X(n+2) binary arrays avoiding patterns 001 and 101 in rows and columns.

108, 640, 3500, 18144, 90552, 439296, 2084940, 9724000, 44710952, 203164416, 914004728, 4077035200, 18052470000, 79420170240, 347424465420, 1512176830560, 6552247686600, 28276211040000, 121580638419240, 521033622457920

Offset: 1

Author

R. H. Hardin Dec 14 2011

Keywords

• nonn

Comments

Diagonal of A202202

Examples

			Some solutions for n=3
..0..1..1..0..0....1..1..0..0..0....0..1..1..1..1....0..1..1..1..0
..1..1..1..1..1....0..1..1..1..0....1..1..1..1..1....1..1..1..1..1
..0..1..1..1..1....0..1..1..0..0....1..1..1..1..1....0..1..1..1..0
..0..1..0..0..0....0..1..1..0..0....1..1..1..0..0....0..1..0..0..0
..0..1..0..0..0....0..1..0..0..0....1..1..0..0..0....0..0..0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..21

Programs

PARI

{a(n) = if(n<1, 0, 4*(n+2)^2 * (2*n+1)!/(n! * (n+1)!))}; /* Michael Somos, Sep 11 2020 */

Formula

Empirical: (n+1)*a(n) -2*(3n+4)*a(n-1) +4*(3n-2)*a(n-2) +8*(3-2n)*a(n-3)=0. - R. J. Mathar, Dec 14 2011

Conjecture: a(n) = 4*(n+2)^2 * (2*n+1)!/(n! * (n+1)!). - Michael Somos, Sep 11 2020