A234220 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 3 (constant-stress 1 X 1 tilings).

104, 436, 1824, 7696, 32384, 137536, 582144, 2488576, 10594304, 45577216, 195108864, 844435456, 3633741824, 15814967296, 68379869184, 299119476736, 1298877906944, 5707511627776, 24878046511104, 109752186044416

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + 20*a(n-2) - 80*a(n-3).

Conjectures from Colin Barker, Oct 13 2018: (Start)

G.f.: 4*x*(26 + 5*x - 500*x^2) / ((1 - 4*x)*(1 - 20*x^2)).

a(n) = 4^(2+n) + 2^(-1+n)*5^((-1+n)/2) * (20-20*(-1)^n+9*sqrt(5)+9*(-1)^n*sqrt(5)).

(End)

Example

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

Crossrefs

Column 1 of A234227.

Sequence in context: A135441 A188150 A234227 * A234208 A372294 A234201

Adjacent sequences: A234217 A234218 A234219 * A234221 A234222 A234223

Keyword

nonn

Author

R. H. Hardin, Dec 21 2013

Status

approved