A202529 Number of (n+2) X 7 binary arrays avoiding patterns 000 and 101 in rows, columns and nw-to-se diagonals.

1940, 4901, 10240, 21297, 46621, 100550, 214388, 460948, 992061, 2128796, 4570909, 9821889, 21095902, 45306296, 97317908, 209034085, 448973976, 964350281, 2071342213, 4449024294, 9556039324, 20525432468, 44086562621, 94693444852

Offset

1,1

Comments

Column 5 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*(1940 + 1021*x + 438*x^2 - 3063*x^3 - 1895*x^4 + 510*x^5 + 976*x^6 + 64*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..0..0..1..1..0..0....0..0..1..1..1..1..1....0..0..1..1..1..1..0
..1..1..1..1..1..1..0....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
..0..1..1..1..1..1..1....1..1..1..1..1..1..0....1..1..1..1..1..1..0
..1..0..0..1..1..0..0....0..1..1..0..0..1..0....1..1..0..0..1..1..0

Crossrefs

Cf. A202532.

Sequence in context: A031542 A214478 A259513 * A236714 A203890 A200656

Adjacent sequences: A202526 A202527 A202528 * A202530 A202531 A202532

Keyword

nonn

Author

R. H. Hardin, Dec 20 2011

Status

approved