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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).
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 05 2014
STATUS
approved