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A223211
3 X 3 X 3 triangular graph coloring a rectangular array: number of n X 1 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
1
6, 18, 60, 192, 624, 2016, 6528, 21120, 68352, 221184, 715776, 2316288, 7495680, 24256512, 78495744, 254017536, 822018048, 2660106240, 8608284672, 27856994304, 90147127296, 291722231808, 944032972800, 3054954872832, 9886041636864
OFFSET
1,1
COMMENTS
Column 1 of A223218.
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) + 4*a(n-2) = 6*A063782(n-1).
Conjectures from Colin Barker, Aug 17 2018: (Start)
G.f.: 6*x*(1 + x) / (1 - 2*x - 4*x^2).
a(n) = (3*((1-sqrt(5))^n*(-3+sqrt(5)) + (1+sqrt(5))^n*(3+sqrt(5)))) / (4*sqrt(5)).
(End)
EXAMPLE
Some solutions for n=3:
..4....4....0....2....1....4....2....3....2....2....0....5....1....3....4....5
..2....1....1....5....2....2....1....1....0....1....1....4....3....4....3....2
..0....4....4....2....0....4....2....0....2....0....0....2....1....1....1....1
CROSSREFS
Cf. A223218.
Sequence in context: A227809 A119106 A223468 * A334330 A144706 A074427
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 18 2013
STATUS
approved