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

1,1

Comments

Diagonal of A202202

Links

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

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

Example

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

Prog

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

Crossrefs

Sequence in context: A129027 A288706 A204276 * A333757 A203373 A292343

Adjacent sequences: A202191 A202192 A202193 * A202195 A202196 A202197

Keyword

nonn

Author

R. H. Hardin Dec 14 2011

Status

approved