A202530 Number of (n+2) X 8 binary arrays avoiding patterns 000 and 101 in rows, columns and nw-to-se diagonals.

4184, 10584, 22118, 45899, 100550, 216973, 462445, 994256, 2140144, 4592250, 9860075, 21187586, 45507845, 97733497, 209931772, 450924056, 968516494, 2080273923, 4468253006, 9597335189, 20614070621, 44276998192, 95102536960

Offset

1,1

Comments

Column 6 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*(4184 + 2216*x + 950*x^2 - 6705*x^3 - 4048*x^4 + 1173*x^5 + 2105*x^6 + 116*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:
..1..1..1..0..0..1..1..0....0..1..0..0..1..1..1..0....0..0..1..1..1..0..0..1
..1..1..1..1..1..1..1..1....1..1..1..1..1..1..1..0....1..1..1..1..1..1..1..1
..1..1..1..1..1..1..1..1....1..1..1..1..1..1..1..1....1..1..1..1..1..1..1..1
..0..1..1..1..1..1..1..0....1..1..1..1..1..1..1..0....1..1..1..1..1..1..1..1
..0..1..0..0..1..1..1..0....1..1..0..0..1..1..0..0....1..1..1..1..0..0..1..1

Crossrefs

Cf. A202532.

Sequence in context: A135953 A290846 A236805 * A242770 A234723 A152511

Adjacent sequences: A202527 A202528 A202529 * A202531 A202532 A202533

Keyword

nonn

Author

R. H. Hardin, Dec 20 2011

Status

approved