A234135 Number of (n+1) X (3+1) 0..3 arrays with every 2 X 2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 9.

192, 296, 488, 968, 1992, 4808, 11336, 30536, 76872, 218696, 567368, 1657928, 4362312, 12916808, 34218056, 101986376, 271073352, 810573896, 2158002248, 6463471688, 17221877832, 51623592008, 137606856776, 412652601416

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 8*a(n-2) - 30*a(n-3) + 4*a(n-4) + 48*a(n-5) - 32*a(n-6).

Empirical g.f.: 8*x*(24 - 35*x - 242*x^2 + 362*x^3 + 412*x^4 - 584*x^5) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)*(1 - 8*x^2)). - Colin Barker, Oct 13 2018

Example

Some solutions for n=5:
  3 0 3 0     0 1 0 1     0 3 0 0     1 1 1 1     3 3 3 3
  2 2 2 2     1 3 1 3     3 3 3 0     3 0 3 0     3 0 3 0
  0 3 0 3     0 1 0 1     3 0 3 3     2 2 2 2     1 1 1 1
  3 3 3 3     3 1 3 1     0 0 0 3     3 0 3 0     3 0 3 0
  0 3 0 3     0 1 0 1     3 0 3 3     1 1 1 1     0 0 0 0
  2 2 2 2     3 1 3 1     3 3 3 0     3 0 3 0     3 0 3 0

Crossrefs

Column 3 of A234140.

Sequence in context: A273890 A344860 A045077 * A030632 A189987 A229361

Adjacent sequences: A234132 A234133 A234134 * A234136 A234137 A234138

Keyword

nonn

Author

R. H. Hardin, Dec 19 2013

Status

approved