|
%I #4 Mar 21 2013 04:43:43
%S 1,3,6,9,19,36,27,115,121,216,81,631,1519,771,1296,243,3539,16323,
%T 20115,4913,7776,729,19759,182901,426359,266419,31307,46656,2187,
%U 110427,2030665,9685063,11148439,3528715,199497,279936,6561,617015,22598167
%N T(n,k)=Petersen graph (3,1) coloring a rectangular array: number of nXk 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0
%C Table starts
%C ........1........3............9..............27.................81
%C ........6.......19..........115.............631...............3539
%C .......36......121.........1519...........16323.............182901
%C ......216......771........20115..........426359............9685063
%C .....1296.....4913.......266419........11148439..........515473927
%C .....7776....31307......3528715.......291545903........27465794119
%C ....46656...199497.....46737819......7624417031......1463848507173
%C ...279936..1271251....619042315....199391762123.....78024299447333
%C ..1679616..8100769...8199214219...5214442630935...4158831849750231
%C .10077696.51620379.108598575915.136366781617267.221674060909378867
%H R. H. Hardin, <a href="/A223504/b223504.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = 6*a(n-1)
%F k=2: a(n) = 7*a(n-1) -4*a(n-2)
%F k=3: a(n) = 15*a(n-1) -24*a(n-2) +10*a(n-3)
%F k=4: a(n) = 31*a(n-1) -127*a(n-2) -20*a(n-3) +705*a(n-4) -1027*a(n-5) +499*a(n-6) -60*a(n-7)
%F k=5: [order 21]
%F k=6: [order 53]
%F Empirical for row n:
%F n=1: a(n) = 3*a(n-1)
%F n=2: a(n) = 5*a(n-1) +4*a(n-2) -4*a(n-3) for n>4
%F n=3: a(n) = 12*a(n-1) -4*a(n-2) -73*a(n-3) +103*a(n-4) -23*a(n-5) -16*a(n-6) +4*a(n-7) for n>8
%F n=4: [order 21] for n>22
%F n=5: [order 60] for n>61
%e Some solutions for n=3 k=4
%e ..0..3..4..1....0..2..1..4....0..3..0..3....0..2..1..2....0..1..4..3
%e ..0..3..4..3....5..2..5..4....4..1..0..1....1..2..0..2....0..1..0..3
%e ..5..3..0..1....1..2..1..2....0..1..0..1....5..2..0..2....0..3..0..1
%Y Column 1 is A000400(n-1)
%Y Column 2 is A138977
%Y Row 1 is A000244(n-1)
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Mar 21 2013
| 