A206981 Number of n X 2 0..1 arrays avoiding the patterns 0 1 0 or 1 0 1 in any row, column, diagonal or antidiagonal.

4, 16, 36, 100, 256, 676, 1764, 4624, 12100, 31684, 82944, 217156, 568516, 1488400, 3896676, 10201636, 26708224, 69923044, 183060900, 479259664, 1254718084, 3284894596, 8599965696, 22515002500, 58945041796, 154320122896, 404015326884

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - a(n-3). G.f.: -4*x*(-1-2*x+x^2) / ( (1+x)*(x^2-3*x+1) ).

Empirical: a(n) = (A080097(n)+1)*4. - Martin Ettl, Nov 13 2012

Example

Some solutions for n=4
..1..1....0..0....0..0....0..0....1..1....0..1....1..1....0..1....1..0....0..0
..0..1....0..1....1..0....1..0....1..1....1..1....1..1....1..0....0..1....1..1
..0..0....1..1....1..1....1..0....1..1....1..0....1..1....1..0....0..1....1..1
..1..0....1..1....0..1....1..0....1..1....1..0....0..0....1..0....1..0....0..0

Crossrefs

Column 2 of A206987.

Cf. A080097.

Sequence in context: A005722 A372635 A075408 * A318149 A233409 A181795

Adjacent sequences: A206978 A206979 A206980 * A206982 A206983 A206984

Keyword

nonn

Author

R. H. Hardin, Feb 14 2012

Status

approved