A234259 Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 2 (constant-stress 1 X 1 tilings).

20, 46, 104, 244, 560, 1336, 3104, 7504, 17600, 42976, 101504, 249664, 592640, 1465216, 3490304, 8660224, 20679680, 51437056, 123029504, 306525184, 733982720, 1830762496, 4387119104, 10951020544, 26255605760, 65571905536, 157265199104

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 6*a(n-2) - 12*a(n-3).

Conjectures from Colin Barker, Oct 14 2018: (Start)

G.f.: 2*x*(10 + 3*x - 54*x^2) / ((1 - 2*x)*(1 - 6*x^2)).

a(n) = 2^(2+n) + 2^((-3+n)/2)*3^((-1+n)/2)*(12-12*(-1)^n+5*sqrt(6)+5*(-1)^n*sqrt(6)).

(End)

Example

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

Crossrefs

Column 1 of A234266.

Sequence in context: A236474 A145220 A234266 * A135286 A338235 A177725

Adjacent sequences: A234256 A234257 A234258 * A234260 A234261 A234262

Keyword

nonn

Author

R. H. Hardin, Dec 22 2013

Status

approved