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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A223599.
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
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