A202527 Number of (n+2) X 5 binary arrays avoiding patterns 000 and 101 in rows, columns and nw-to-se diagonals.

417, 1084, 2263, 4669, 10240, 22118, 47098, 101249, 218000, 467743, 1004221, 2157988, 4635082, 9954218, 21381733, 45927212, 98644463, 211878013, 455096536, 977499190, 2099565274, 4509660401, 9686297296, 20805178151, 44687426189

Offset

1,1

Comments

Column 3 of A202532.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 2*a(n-1) +2*a(n-3) -2*a(n-4) -2*a(n-5) +a(n-7) for n>8.

Empirical g.f.: x*(417 + 250*x + 95*x^2 - 691*x^3 - 432*x^4 + 114*x^5 + 218*x^6 + 20*x^7) / ((1 - x)*(1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - Colin Barker, Jun 01 2018

Example

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

Crossrefs

Cf. A202532.

Sequence in context: A223422 A239191 A324613 * A224557 A080467 A292422

Adjacent sequences: A202524 A202525 A202526 * A202528 A202529 A202530

Keyword

nonn

Author

R. H. Hardin, Dec 20 2011

Status

approved