A202525 Number of (n+2) X 3 binary arrays avoiding patterns 000 and 101 in rows, columns and nw-to-se diagonals.

86, 198, 417, 890, 1940, 4184, 8994, 19420, 41918, 90355, 194874, 420410, 906707, 1955533, 4217976, 9097605, 19621946, 42321918, 91282656, 196883149, 424648818, 915907828, 1975482000, 4260832180, 9190009191, 19821539577, 42752232438

Offset

1,1

Comments

Column 1 of A202532.

Links

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

Formula

Empirical: a(n) = a(n-1) +6*a(n-3) +a(n-5) -7*a(n-6) -3*a(n-7) -a(n-8) +2*a(n-9) +a(n-10).

Empirical g.f.: x*(86 + 112*x + 219*x^2 - 43*x^3 - 138*x^4 - 344*x^5 - 126*x^6 + 13*x^7 + 103*x^8 + 40*x^9) / ((1 + x^2 - x^3)*(1 - x - x^2 - 4*x^3 + 2*x^5 + 3*x^6 + x^7)). - Colin Barker, Jun 01 2018

Example

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

Crossrefs

Cf. A202532.

Sequence in context: A044418 A044799 A202532 * A202777 A202770 A184095

Adjacent sequences: A202522 A202523 A202524 * A202526 A202527 A202528

Keyword

nonn

Author

R. H. Hardin, Dec 20 2011

Status

approved