A223594 Petersen graph (8,2) coloring a rectangular array: number of n X 3 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph.

144, 1504, 16192, 176224, 1931968, 21308000, 236213312, 2629972704, 29389265856, 329426847840, 3702023397952, 41690675717344, 470324275582912, 5313486488316000, 60099803562912832, 680431871048616672

Offset

1,1

Comments

Column 3 of A223599.

Links

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

Formula

Empirical: a(n) = 23*a(n-1) - 153*a(n-2) + 217*a(n-3) + 258*a(n-4) - 456*a(n-5) - 104*a(n-6) + 192*a(n-7).

Empirical g.f.: 16*x*(9 - 113*x + 227*x^2 + 167*x^3 - 458*x^4 - 64*x^5 + 192*x^6) / (1 - 23*x + 153*x^2 - 217*x^3 - 258*x^4 + 456*x^5 + 104*x^6 - 192*x^7). - Colin Barker, Aug 21 2018

Example

Some solutions for n=3:
..4..5..4....9..1..9....2.10..8....5..6..5....9.15..9....5.13..5....8.10.12
..4..5..4....0..1..2....8.10..8....5..4..5...13.11..9...11.13..5....2.10..2
..4..5..4....0..1..9....8.14..8....3..4..3...13.15..9...15.13..5....2.10.12

Crossrefs

Cf. A223599.

Sequence in context: A137416 A109117 A209205 * A223445 A186934 A356731

Adjacent sequences: A223591 A223592 A223593 * A223595 A223596 A223597

Keyword

nonn

Author

R. H. Hardin, Mar 23 2013

Status

approved