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A223434 Generalized Petersen graph (8,2) coloring a rectangular array: number of n X 2 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 or vertical neighbor moves along an edge of this graph. 2

%I #7 Mar 16 2018 07:23:54

%S 48,256,1376,7424,40160,217600,1180256,6405888,34782688,188912640,

%T 1026197344,5575016704,30289360608,164570543616,894181114976,

%U 4858543170304,26399224399840,143442922485760,779415220762976

%N Generalized Petersen graph (8,2) coloring a rectangular array: number of n X 2 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 or vertical neighbor moves along an edge of this graph.

%C Column 2 of A223440.

%H R. H. Hardin, <a href="/A223434/b223434.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) - 11*a(n-2) - 16*a(n-3).

%F Empirical g.f.: 16*x*(3 - 8*x - 9*x^2) / (1 - 8*x + 11*x^2 + 16*x^3). - _Colin Barker_, Mar 16 2018

%e Some solutions for n=3:

%e ..6..5....8..0....3..4...11.13....7..0...11.13....9..1....1..0....1..9....1..9

%e .14..6....0..7....2..3...13.15...15..7...13.15....1..2....0..1....2..1....9.11

%e ..8.14....8..0....3..2...15.13....9.15...15..7....2..3....1..2....3..2....1..9

%Y Cf. A223440.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 20 2013

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