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.

27, 1089, 44217, 1795473, 72906921, 2960456193, 120212193177, 4881332621169, 198211242377097, 8048559615522273, 326819564358379641, 13270825184845208913, 538874719548919491177, 21881530298548175795649

Offset

1,1

Comments

Column 4 of A223556.

Links

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

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

Adjacent sequences: A223549 A223550 A223551 * A223553 A223554 A223555

Keyword

nonn

Author

R. H. Hardin, Mar 22 2013

Status

approved