A234877 Number of (n+1) X (3+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 1, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

128, 268, 472, 1116, 2096, 5316, 10240, 27060, 52744, 142876, 280240, 770572, 1516768, 4208188, 8300136, 23151620, 45717872, 127927396, 252795808, 708714660, 1401057032, 3932335452, 7775722672, 21838955052, 43190207392, 121354286332

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 11*a(n-2) - 23*a(n-3) - 38*a(n-4) + 87*a(n-5) + 46*a(n-6) - 130*a(n-7) - 16*a(n-8) + 78*a(n-9) - 16*a(n-11).

Empirical g.f.: 4*x*(32 + 3*x - 368*x^2 + 42*x^3 + 1425*x^4 - 312*x^5 - 2262*x^6 + 492*x^7 + 1496*x^8 - 192*x^9 - 344*x^10) / ((1 - x)*(1 - x - x^2)*(1 - 4*x^2 + 2*x^4)*(1 - 7*x^2 + 8*x^4)). - Colin Barker, Oct 16 2018

Example

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

Crossrefs

Column 3 of A234882.

Sequence in context: A355919 A235059 A045053 * A229360 A086059 A220582

Adjacent sequences: A234874 A234875 A234876 * A234878 A234879 A234880

Keyword

nonn

Author

R. H. Hardin, Jan 01 2014

Status

approved