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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

R. H. Hardin, Table of n, a(n) for n = 1..210

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: A012116 A157551 A157570 * A157233 A292350 A188976

Adjacent sequences:  A223496 A223497 A223498 * A223500 A223501 A223502

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 21 2013

STATUS

approved

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Last modified September 27 12:30 EDT 2020. Contains 337380 sequences. (Running on oeis4.)