A234557 Number of (n+1) X (1+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4 (constant-stress 1 X 1 tilings).

70, 220, 618, 1954, 5506, 17518, 49506, 158518, 449170, 1447510, 4111458, 13334374, 37954546, 123863638, 353202306, 1159606918, 3311711890, 10935135670, 31268536098, 103805608294, 297121857586, 991365572758, 2839736979906

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 18*a(n-2) - 54*a(n-3) - 80*a(n-4) + 240*a(n-5).

Empirical g.f.: 2*x*(35 + 5*x - 651*x^2 - 40*x^3 + 3000*x^4) / ((1 - 3*x)*(1 - 8*x^2)*(1 - 10*x^2)). - Colin Barker, Oct 15 2018

Example

Some solutions for n=5:
  3 4   2 3   1 3   0 0   2 1   2 2   4 4   3 3   3 3   4 3
  3 0   4 1   3 1   0 4   0 3   0 4   0 4   4 0   0 4   0 3
  1 2   2 3   1 3   2 2   1 0   3 3   2 2   0 0   4 4   4 3
  4 1   3 0   3 1   4 0   0 3   4 0   0 4   4 0   0 4   0 3
  1 2   1 2   1 3   1 1   4 3   3 3   3 3   4 4   2 2   3 2
  4 1   4 1   2 0   4 0   0 3   0 4   0 4   4 0   4 0   0 3

Crossrefs

Column 1 of A234564.

Sequence in context: A235310 A235303 A234564 * A245857 A227879 A072596

Adjacent sequences: A234554 A234555 A234556 * A234558 A234559 A234560

Keyword

nonn

Author

R. H. Hardin, Dec 28 2013

Status

approved