A234414 Number of (n+1) X (1+1) 0..7 arrays with every 2 X 2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.

106, 550, 2848, 14794, 76996, 401332, 2094334, 10939294, 57181342, 299074768, 1565010838, 8192728552, 42902476216, 224726079286, 1177392512218, 6169767623782, 32335691922208, 169492250976178, 888510183018244

Offset

1,1

Links

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

Formula

Empirical: a(n) = 13*a(n-1) - 54*a(n-2) + 57*a(n-3) + 90*a(n-4) - 96*a(n-5) - 108*a(n-6) - 24*a(n-7).

Empirical g.f.: 2*x*(53 - 414*x + 711*x^2 + 714*x^3 - 1212*x^4 - 1200*x^5 - 264*x^6) / (1 - 13*x + 54*x^2 - 57*x^3 - 90*x^4 + 96*x^5 + 108*x^6 + 24*x^7). - Colin Barker, Oct 14 2018

Example

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

Crossrefs

Column 1 of A234421.

Sequence in context: A260937 A200868 A234421 * A090037 A187588 A051974

Adjacent sequences: A234411 A234412 A234413 * A234415 A234416 A234417

Keyword

nonn

Author

R. H. Hardin, Dec 25 2013

Status

approved