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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A223556.
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)
Comments