A223243 3-loop graph coloring a rectangular array: number of n X 4 0..6 arrays where 0..6 label nodes of a graph with edges (0,1), (1,2), (2,0), (0,3), (3,4), (4,0), (0,5), (5,6), and (6,0), and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

168, 4086, 144582, 5336844, 198634758, 7399451382, 275682413748, 10271315554206, 382687513971798, 14258133000231516, 531228116681596086, 19792445044329718422, 737424976053389046756, 27474907428586558064526

Offset

1,1

Comments

Column 4 of A223247.

Links

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

Formula

Empirical: a(n) = 40*a(n-1) - 80*a(n-2) - 869*a(n-3) + 1566*a(n-4) + 1650*a(n-5) - 1796*a(n-6) for n>7.

Empirical g.f.: 6*x*(28 - 439*x - 903*x^2 + 4406*x^3 + 2534*x^4 - 4256*x^5 + 160*x^6) / (1 - 40*x + 80*x^2 + 869*x^3 - 1566*x^4 - 1650*x^5 + 1796*x^6). - Colin Barker, Aug 17 2018

Example

Some solutions for n=3:
..0..2..0..3....1..2..0..1....0..1..0..1....0..1..2..0....1..2..0..2
..3..0..2..0....2..0..4..0....4..0..4..0....1..2..0..4....2..0..1..0
..0..6..0..2....0..2..0..1....0..6..0..4....0..1..2..0....0..3..0..3

Crossrefs

Cf. A223247.

Sequence in context: A360623 A331908 A231995 * A282614 A003807 A011785

Adjacent sequences: A223240 A223241 A223242 * A223244 A223245 A223246

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved