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A223552
Petersen graph (3,1) coloring a rectangular array: number of n X 4 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.
1
27, 1089, 44217, 1795473, 72906921, 2960456193, 120212193177, 4881332621169, 198211242377097, 8048559615522273, 326819564358379641, 13270825184845208913, 538874719548919491177, 21881530298548175795649
OFFSET
1,1
COMMENTS
Column 4 of A223556.
LINKS
FORMULA
Empirical: a(n) = 41*a(n-1) - 16*a(n-2).
Conjectures from Colin Barker, Aug 21 2018: (Start)
G.f.: 9*x*(3 - 2*x) / (1 - 41*x + 16*x^2).
a(n) = 3*sqrt(3/11)*2^(-4-n)*((41-7*sqrt(33))^n*(-1+sqrt(33)) + (1+sqrt(33))*(41+7*sqrt(33))^n).
(End)
EXAMPLE
Some solutions for n=3:
..0..2..0..2....0..1..2..5....0..2..0..2....0..2..1..4....0..1..0..1
..0..1..0..2....2..1..4..5....1..2..0..2....5..4..5..2....2..1..2..1
..4..1..0..2....4..3..4..5....5..3..5..4....5..2..1..0....4..1..4..3
CROSSREFS
Cf. A223556.
Sequence in context: A222440 A159457 A290946 * A357228 A104206 A327596
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 22 2013
STATUS
approved