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A223692 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 or antidiagonal neighbor moves along an edge of this graph 13

%I #8 Jul 28 2013 17:41:37

%S 16,48,256,144,432,4096,432,2304,3888,65536,1296,12384,37008,34992,

%T 1048576,3888,66816,363600,595584,314928,16777216,11664,361440,

%U 3788640,10817856,9594000,2834352,268435456,34992,1958400,40075632,223096320

%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 or antidiagonal neighbor moves along an edge of this graph

%C Table starts

%C ............16..........48............144..............432.................1296

%C ...........256.........432...........2304............12384................66816

%C ..........4096........3888..........37008...........363600..............3788640

%C .........65536.......34992.........595584.........10817856............223096320

%C .......1048576......314928........9594000........324280368..........13402129824

%C ......16777216.....2834352......154616832.......9762152544.........814399853760

%C .....268435456....25509168.....2492365968.....294583794768.......49817845241568

%C ....4294967296...229582512....40180445568....8901308553408.....3059068970173824

%C ...68719476736..2066242608...647800215696..269168305340592...188252023352797728

%C .1099511627776.18596183472.10444288589568.8142829402619232.11599193857488796224

%H R. H. Hardin, <a href="/A223692/b223692.txt">Table of n, a(n) for n = 1..218</a>

%F Empirical for column k:

%F k=1: a(n) = 16*a(n-1)

%F k=2: a(n) = 9*a(n-1)

%F k=3: a(n) = 24*a(n-1) -127*a(n-2)

%F k=4: a(n) = 59*a(n-1) -1103*a(n-2) +7621*a(n-3) -16900*a(n-4)

%F k=5: [order 7] for n>8

%F k=6: [order 17]) for n>18

%F k=7: [order 37] for n>39

%F Empirical for row n:

%F n=1: a(n) = 3*a(n-1)

%F n=2: a(n) = 8*a(n-1) -11*a(n-2) -16*a(n-3) for n>4

%F n=3: a(n) = [order 10]) for n>12

%F n=4: a(n) = [order 24] for n>27

%F n=5: a(n) = [order 56] for n>61

%e Some solutions for n=3 k=4

%e ..2..1..9..1....6..5..4..5....6.14..6.14....4..3..2.10....2..3..4..3

%e ..2..1..9.11....4..5..6.14...12.14..8.14....2.10..2.10....4..3.11.13

%e ..9.11..9.15....6..7..6.14....8..0..8..0....8.10..8.10...11.13.11..9

%Y Column 1 is A001025

%Y Column 2 is 48*9^(n-1)

%Y Row 1 is A188825(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 25 2013

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Last modified March 5 02:31 EST 2024. Contains 370537 sequences. (Running on oeis4.)