A213413 Half the number of n X 3 binary arrays with no 3 X 3 submatrix formed with any three rows and columns equal to J-I.

4, 32, 253, 1970, 15109, 114302, 854473, 6323090, 46390429, 337896422, 2446208593, 17618827610, 126352826149, 902840120942, 6431323577113, 45694024938530, 323937251540269, 2292187810495862, 16193839911208033, 114251845502143850

Offset

1,1

Comments

Column 3 of A213418.

Links

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

Formula

a(n) = (5^n - 3*6^n + 3*7^n)/2.

a(n) = 18*a(n-1) - 107*a(n-2) + 210*a(n-3).

G.f.: x*(4 - 40*x + 105*x^2) / ((1 - 5*x)*(1 - 6*x)*(1 - 7*x)). - Colin Barker, Jul 21 2018

Example

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

Crossrefs

Cf. A213418.

Sequence in context: A303416 A007278 A108449 * A317512 A300177 A013731

Adjacent sequences: A213410 A213411 A213412 * A213414 A213415 A213416

Keyword

nonn

Author

R. H. Hardin and N. J. A. Sloane, Jun 10 2012

Status

approved