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A223594
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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.
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%I #8 Aug 21 2018 10:04:26
%S 144,1504,16192,176224,1931968,21308000,236213312,2629972704,
%T 29389265856,329426847840,3702023397952,41690675717344,
%U 470324275582912,5313486488316000,60099803562912832,680431871048616672
%N 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.
%C Column 3 of A223599.
%H R. H. Hardin, <a href="/A223594/b223594.txt">Table of n, a(n) for n = 1..210</a>
%F 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).
%F 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
%e Some solutions for n=3:
%e ..4..5..4....9..1..9....2.10..8....5..6..5....9.15..9....5.13..5....8.10.12
%e ..4..5..4....0..1..2....8.10..8....5..4..5...13.11..9...11.13..5....2.10..2
%e ..4..5..4....0..1..9....8.14..8....3..4..3...13.15..9...15.13..5....2.10.12
%Y Cf. A223599.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 23 2013
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