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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).
1
104, 436, 1824, 7696, 32384, 137536, 582144, 2488576, 10594304, 45577216, 195108864, 844435456, 3633741824, 15814967296, 68379869184, 299119476736, 1298877906944, 5707511627776, 24878046511104, 109752186044416
OFFSET
1,1
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 21 2013
STATUS
approved