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A223440 T(n,k)=Generalized Petersen graph (8,2) coloring a rectangular array: number of nXk 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.

%I A223440 #6 Jul 23 2025 04:09:59
%S A223440 16,48,48,144,256,144,432,1376,1376,432,1296,7424,14112,7424,1296,
%T A223440 3888,40160,147520,147520,40160,3888,11664,217600,1562176,3099264,
%U A223440 1562176,217600,11664,34992,1180256,16693920,67182208,67182208,16693920,1180256
%N A223440 T(n,k)=Generalized Petersen graph (8,2) coloring a rectangular array: number of nXk 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 A223440 Table starts
%C A223440 .....16........48..........144.............432...............1296
%C A223440 .....48.......256.........1376............7424..............40160
%C A223440 ....144......1376........14112..........147520............1562176
%C A223440 ....432......7424.......147520.........3099264...........67182208
%C A223440 ...1296.....40160......1562176........67182208.........3049973040
%C A223440 ...3888....217600.....16693920......1485628224.......142702806112
%C A223440 ..11664...1180256....179532768.....33277934848......6790055219264
%C A223440 ..34992...6405888...1939216640....751557814208....326095786136512
%C A223440 .104976..34782688..21008925952..17060996532992..15740601974728144
%C A223440 .314928.188912640.228065409888.388541047749184.761894144429277728
%H A223440 R. H. Hardin, <a href="/A223440/b223440.txt">Table of n, a(n) for n = 1..220</a>
%F A223440 Empirical for column k:
%F A223440 k=1: a(n) = 3*a(n-1)
%F A223440 k=2: a(n) = 8*a(n-1) -11*a(n-2) -16*a(n-3)
%F A223440 k=3: a(n) = 15*a(n-1) -18*a(n-2) -310*a(n-3) +167*a(n-4) +475*a(n-5) -244*a(n-6) -100*a(n-7) +48*a(n-8)
%F A223440 k=4: [order 14]
%F A223440 k=5: [order 36]
%F A223440 k=6: [order 75]
%e A223440 Some solutions for n=3 k=4
%e A223440 ..7.15..7..0....1..0..7..0...10..8.14.12....8.14.12.10....9..1..9.11
%e A223440 ..6..7..6..7....2..1..0..7...12.10.12.14...14.12.10..8....1..9.11..9
%e A223440 ..7.15..7.15...10..2..1..0...14..8.14..8....8.14.12.14....9..1..9..1
%Y A223440 Column 1 is A188825(n+1)
%K A223440 nonn,tabl
%O A223440 1,1
%A A223440 _R. H. Hardin_ Mar 20 2013