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A223499 Petersen graph (3,1) coloring a rectangular array: number of n X 3 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, diagonal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0. 1
9, 115, 1519, 20115, 266419, 3528715, 46737819, 619042315, 8199214219, 108598575915, 1438387920619, 19051445129515, 252336352607019, 3342194485203115, 44267359266773419, 586321084882796715 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 3 of A223504.
LINKS
FORMULA
Empirical: a(n) = 15*a(n-1) - 24*a(n-2) + 10*a(n-3).
Conjectures from Colin Barker, Aug 21 2018: (Start)
G.f.: x*(9 - 20*x + 10*x^2) / ((1 - x)*(1 - 14*x + 10*x^2)).
a(n) = (13 + (13-2*sqrt(39))*(7-sqrt(39))^n + (7+sqrt(39))^n*(13+2*sqrt(39))) / 39.
(End)
EXAMPLE
Some solutions for n=3:
..0..1..4....0..3..4....0..1..4....0..2..5....0..1..4....0..3..4....0..3..0
..0..3..0....4..3..5....2..1..0....0..3..0....4..3..0....4..3..4....4..3..0
..5..2..5....5..3..4....4..1..4....0..1..0....0..3..4....5..3..4....5..3..0
CROSSREFS
Cf. A223504.
Sequence in context: A356240 A157551 A157570 * A362774 A157233 A292350
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 21 2013
STATUS
approved

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Last modified February 21 20:23 EST 2024. Contains 370237 sequences. (Running on oeis4.)