A235282 Number of (n+1) X (1+1) 0..3 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4 (constant-stress 1 X 1 tilings).

20, 40, 68, 136, 236, 472, 836, 1672, 3020, 6040, 11108, 22216, 41516, 83032, 157316, 314632, 603020, 1206040, 2333348, 4666696, 9097196, 18194392, 35680196, 71360392, 140595020, 281190040, 556002788, 1112005576, 2204879276, 4409758552

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 6*a(n-3).

Conjectures from Colin Barker, Oct 18 2018: (Start)

G.f.: 4*x*(5 - 18*x^2) / ((1 - 2*x)*(1 - 3*x^2)).

a(n) = 2^(2+n) + 2*3^((-1+n)/2)*(3-3*(-1)^n + 2*sqrt(3) + 2*(-1)^n*sqrt(3)).

(End)

Example

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

Crossrefs

Column 1 of A235289.

Sequence in context: A065607 A008602 A061830 * A270296 A338433 A347368

Adjacent sequences: A235279 A235280 A235281 * A235283 A235284 A235285

Keyword

nonn

Author

R. H. Hardin, Jan 05 2014

Status

approved