A235081 Number of (n+1) X (2+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

90, 198, 418, 930, 2002, 4514, 9838, 22402, 49294, 113086, 250886, 579046, 1294282, 3002798, 6759506, 15755762, 35708898, 83589666, 190685374, 448116834, 1028599870, 2425881086, 5600857366, 13251905638, 30761769178, 72994149742

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 10*a(n-2) - 33*a(n-3) - 28*a(n-4) + 111*a(n-5) + 20*a(n-6) - 111*a(n-7) - 27*a(n-8) + 30*a(n-9) + 10*a(n-10).

Empirical g.f.: 2*x*(45 - 36*x - 538*x^2 + 333*x^3 + 2043*x^4 - 722*x^5 - 2554*x^6 - 257*x^7 + 772*x^8 + 226*x^9) / ((1 - x - x^2)*(1 - 2*x - x^2)*(1 - 5*x^2)*(1 - 5*x^2 + 2*x^4)). - Colin Barker, Oct 17 2018

Example

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

Crossrefs

Column 2 of A235087.

Sequence in context: A282473 A044422 A044803 * A074213 A231961 A237131

Adjacent sequences: A235078 A235079 A235080 * A235082 A235083 A235084

Keyword

nonn

Author

R. H. Hardin, Jan 03 2014

Status

approved