A186563 Number of (n+2) X 6 0..2 arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.

6594, 1411, 3421, 8983, 11557, 12895, 14845, 18415, 25381, 40279, 63565, 102591, 161381, 244087, 372205, 569647, 861493, 1322215, 2039165, 3110335, 4775493, 7347991, 11212621, 17186671, 26409301, 40358535, 61856925, 94997471, 145320485

Offset

1,1

Comments

Column 4 of A186568.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 4*a(n-4) + 2*a(n-5) + 2*a(n-6) - 2*a(n-7) for n>12.

Empirical g.f.: x*(6594 - 11777*x + 7193*x^2 - 9636*x^3 + 20566*x^4 - 15622*x^5 - 19680*x^6 + 17962*x^7 + 1848*x^8 - 4416*x^9 + 6272*x^11) / ((1 - x)*(1 - x - 2*x^3 + 2*x^4 - 2*x^6)). - Colin Barker, Apr 18 2018

Example

Some solutions for 4 X 6:
  1 0 0 0 0 2   1 0 0 0 2 1   2 0 0 0 2 0   0 0 0 0 0 2
  0 0 0 0 0 0   0 0 0 0 0 0   0 0 0 0 0 0   0 0 0 0 0 0
  0 0 0 0 0 0   0 0 0 0 0 0   0 0 0 0 0 0   2 0 0 0 0 0
  0 2 0 0 0 0   0 1 0 0 0 0   0 1 0 0 0 0   1 2 0 0 0 0

Crossrefs

Cf. A186568.

Sequence in context: A319604 A256837 A216177 * A252637 A164971 A214434

Adjacent sequences: A186560 A186561 A186562 * A186564 A186565 A186566

Keyword

nonn

Author

R. H. Hardin, Feb 23 2011

Status

approved