A223558 Petersen graph (3,1) coloring a rectangular array: number of 3 X n 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.
36, 243, 3249, 44217, 609309, 8410671, 116124291, 1603350909, 22137868197, 305663255847, 4220371688499, 58271764766661, 804573346481541, 11108952552823119, 153384184751908707, 2117815160357837997
Offset: 1
Keywords
Examples
Some solutions for n=3: ..0..2..0....0..3..0....0..1..4....0..3..4....0..3..5....0..1..2....0..1..0 ..5..2..5....5..2..1....2..5..3....0..3..4....5..4..3....2..5..4....4..3..5 ..5..3..5....5..4..3....4..5..2....0..3..4....3..0..3....2..1..4....0..3..4
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A223556.
Formula
Empirical: a(n) = 17*a(n-1) - 47*a(n-2) + 41*a(n-3) - 10*a(n-4) for n>6.
Empirical g.f.: 9*x*(4 - 41*x + 90*x^2 - 119*x^3 + 80*x^4 - 18*x^5) / ((1 - x)*(1 - 16*x + 31*x^2 - 10*x^3)). - Colin Barker, Aug 21 2018
Comments