A185791 Number of (n+1) X 3 binary arrays with no 2 X 2 subblock sum equal to any horizontal or vertical neighbor 2 X 2 subblock sum.

40, 96, 224, 576, 1408, 3456, 8320, 20864, 50816, 125312, 304768, 756096, 1844864, 4548992, 11110016, 27429248, 67069568, 165194112, 404309632, 995805568, 2438669952, 6000273792, 14703462016, 36167944576, 88660698752, 217982249344

Offset

1,1

Comments

Column 2 of A185798.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = a(n-1) + 2*a(n-2) + 16*a(n-4) - 16*a(n-5).

Empirical g.f.: 8*x*(5 + 7*x + 6*x^2 + 20*x^3 - 32*x^4) / (1 - x - 2*x^2 - 16*x^4 + 16*x^5). - Colin Barker, Apr 16 2018

Example

Some solutions for 5 X 3:
..0..1..0....1..1..1....1..0..0....0..0..1....0..0..0....0..0..1....0..1..1
..1..0..0....0..1..1....0..0..0....0..0..1....1..1..0....0..0..1....0..1..1
..0..0..0....0..0..1....0..0..1....0..1..1....1..0..1....1..1..1....0..0..0
..0..0..1....0..0..0....1..0..1....0..1..1....0..1..1....1..0..0....1..1..0
..0..1..1....1..0..0....0..1..1....0..0..0....0..0..0....0..0..0....1..0..1

Crossrefs

Cf. A185798.

Sequence in context: A279689 A063310 A211493 * A092889 A235280 A235271

Adjacent sequences: A185788 A185789 A185790 * A185792 A185793 A185794

Keyword

nonn

Author

R. H. Hardin, Feb 04 2011

Status

approved