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%I #4 Mar 23 2013 06:09:09
%S 16,48,256,144,256,4096,432,1504,1376,65536,1296,6736,16192,7424,
%T 1048576,3888,32768,122608,176224,40160,16777216,11664,156592,1124064,
%U 2372080,1931968,217600,268435456,34992,755200,9902320,43725920,47659632
%N T(n,k)=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, diagonal or antidiagonal neighbor moves along an edge of this graph
%C Table starts
%C ............16........48..........144.............432...............1296
%C ...........256.......256.........1504............6736..............32768
%C ..........4096......1376........16192..........122608............1124064
%C .........65536......7424.......176224.........2372080...........43725920
%C .......1048576.....40160......1931968........47659632.........1807461152
%C ......16777216....217600.....21308000.......982848688........77164934624
%C .....268435456...1180256....236213312.....20631729648......3355919411936
%C ....4294967296...6405888...2629972704....438231627440....147579242411936
%C ...68719476736..34782688..29389265856...9379905920496...6534353238114336
%C .1099511627776.188912640.329426847840.201754894742320.290550417324168160
%H R. H. Hardin, <a href="/A223599/b223599.txt">Table of n, a(n) for n = 1..161</a>
%F Empirical for column k:
%F k=1: a(n) = 16*a(n-1)
%F k=2: a(n) = 8*a(n-1) -11*a(n-2) -16*a(n-3)
%F k=3: 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 k=4: [order 9]
%F k=5: [order 29]
%F k=6: [order 55]
%F Empirical for row n:
%F n=1: a(n) = 3*a(n-1)
%F n=2: a(n) = 6*a(n-1) +3*a(n-2) -42*a(n-3) -8*a(n-4) +48*a(n-5) for n>6
%F n=3: [order 11] for n>12
%F n=4: [order 28] for n>29
%F n=5: [order 74] for n>75
%e Some solutions for n=3 k=4
%e .14..6..5.13...13.15..9.15...12..4.12.10....6..5.13.15....8.14..8.10
%e ..7..6..5..6...13.15..9..1...12..4.12..4....6..5.13..5....8.14..8.14
%e ..5..6.14..6....9.15..9.11....5..4.12.14...13..5..6..5....6.14..6.14
%Y Column 1 is A001025
%Y Column 2 is A223434
%Y Row 1 is A188825(n+1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Mar 23 2013
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