A186561 Number of (n+2) X 4 0..2 arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.

721, 173, 401, 1411, 2617, 3379, 4033, 4795, 6361, 10443, 17153, 26995, 43177, 66139, 98497, 151699, 231881, 350539, 543249, 835843, 1270105, 1958875, 3007777, 4577331, 7041321, 10810763, 16490033, 25335715, 38890105, 59403259, 91177217

Offset

1,1

Comments

Column 2 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>10.

Empirical g.f.: x*(721 - 1269*x + 776*x^2 - 660*x^3 + 2734*x^4 - 1996*x^5 - 3114*x^6 + 812*x^7 + 1236*x^8 + 712*x^9) / ((1 - x)*(1 - x - 2*x^3 + 2*x^4 - 2*x^6)). - Colin Barker, Apr 18 2018

Example

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

Crossrefs

Cf. A186568.

Sequence in context: A172727 A283048 A282021 * A119451 A119452 A034179

Adjacent sequences: A186558 A186559 A186560 * A186562 A186563 A186564

Keyword

nonn

Author

R. H. Hardin, Feb 23 2011

Status

approved