A234875 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 1, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

32, 68, 128, 268, 512, 1068, 2048, 4268, 8192, 17068, 32768, 68268, 131072, 273068, 524288, 1092268, 2097152, 4369068, 8388608, 17476268, 33554432, 69905068, 134217728, 279620268, 536870912, 1118481068, 2147483648, 4473924268

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-2) - 4*a(n-4).

Conjectures from Colin Barker, Oct 16 2018: (Start)

G.f.: 4*x*(8 + 17*x - 8*x^2 - 18*x^3) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + 2*x)).

a(n) = (4 + (-2)^n + 49*2^n) / 3 for n even.

a(n) = ((-2)^n + 49*2^n) / 3 for n odd.

(End)

Example

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

Crossrefs

Column 1 of A234882.

Sequence in context: A043935 A044134 A044515 * A153981 A264589 A100017

Adjacent sequences: A234872 A234873 A234874 * A234876 A234877 A234878

Keyword

nonn

Author

R. H. Hardin, Jan 01 2014

Status

approved