A234731 Number of (n+1) X (1+1) 0..7 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 8 (constant-stress 1 X 1 tilings).

168, 672, 2184, 8736, 29976, 119904, 426120, 1704480, 6197208, 24788832, 91531464, 366125856, 1366929816, 5467719264, 20584483080, 82337932320, 312012926808, 1248051707232, 4754424175944, 19017696703776, 72763338316056

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + 34*a(n-2) - 136*a(n-3) - 369*a(n-4) + 1476*a(n-5) + 1260*a(n-6) - 5040*a(n-7).

Empirical g.f.: 24*x*(7 - 259*x^2 + 3090*x^4 - 11760*x^6) / ((1 - 4*x)*(1 - 7*x^2)*(1 - 12*x^2)*(1 - 15*x^2)). - Colin Barker, Oct 16 2018

Example

Some solutions for n=5:
  1 7   7 2   1 5   2 6   7 2   0 4   3 6   1 5   7 3   5 0
  4 2   2 5   5 1   5 1   4 7   4 0   7 2   4 0   0 4   0 3
  0 6   5 0   3 7   2 6   6 1   2 6   2 5   3 7   4 0   6 1
  3 1   1 4   7 3   5 1   3 6   4 0   6 1   4 0   0 4   2 5
  1 7   7 2   0 4   1 5   5 0   0 4   3 6   2 6   4 0   7 2
  5 3   1 4   7 3   7 3   0 3   4 0   5 0   5 1   2 6   0 3

Crossrefs

Column 1 of A234738.

Sequence in context: A137863 A266808 A234738 * A157998 A234823 A234816

Adjacent sequences: A234728 A234729 A234730 * A234732 A234733 A234734

Keyword

nonn

Author

R. H. Hardin, Dec 30 2013

Status

approved