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A230269 Number of n X 2 0..2 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero. 3
0, 0, 2, 8, 30, 108, 386, 1376, 4902, 17460, 62186, 221480, 788814, 2809404, 10005842, 35636336, 126920694, 452034756, 1609945658, 5733906488, 20421610782, 72732645324, 259041157538, 922588763264, 3285848604870, 11702723341140 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Column 2 of A230275.
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) - a(n-2) - 2*a(n-3).
Conjectures from Colin Barker, Feb 24 2018: (Start)
G.f.: 2*x^3 / ((1 - x)*(1 - 3*x - 2*x^2)).
a(n) = -1/2 + (2^(-2-n)*(-(-5+sqrt(17))*(3+sqrt(17))^n - (3-sqrt(17))^n*(5+sqrt(17)))) / sqrt(17).
(End)
EXAMPLE
All solutions for n=3:
..0..2....0..1
..1..1....2..2
..2..0....1..0
CROSSREFS
Cf. A230275.
Sequence in context: A168605 A127865 A199923 * A278023 A077839 A052530
KEYWORD
nonn
AUTHOR
R. H. Hardin, Oct 14 2013
STATUS
approved

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Last modified July 13 12:04 EDT 2024. Contains 374282 sequences. (Running on oeis4.)