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

16, 48, 256, 144, 432, 4096, 432, 2304, 3888, 65536, 1296, 12384, 37008, 34992, 1048576, 3888, 66816, 363600, 595584, 314928, 16777216, 11664, 361440, 3788640, 10817856, 9594000, 2834352, 268435456, 34992, 1958400, 40075632, 223096320, 324280368, 154616832, 25509168, 4294967296

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..218

Formula

Empirical for column k:

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

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

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

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

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

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

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

Empirical for row n:

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

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

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

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

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

Example

Table starts:
          16,        48,         144,           432,             1296, ...
         256,       432,        2304,         12384,            66816, ...
        4096,      3888,       37008,        363600,          3788640, ...
       65536,     34992,      595584,      10817856,        223096320, ...
     1048576,    314928,     9594000,     324280368,      13402129824, ...
    16777216,   2834352,   154616832,    9762152544,     814399853760, ...
   268435456,  25509168,  2492365968,  294583794768,   49817845241568, ...
  4294967296, 229582512, 40180445568, 8901308553408, 3059068970173824, ...
Some solutions for n=3 k=4
..2..1..9..1....6..5..4..5....6.14..6.14....4..3..2.10....2..3..4..3
..2..1..9.11....4..5..6.14...12.14..8.14....2.10..2.10....4..3.11.13
..9.11..9.15....6..7..6.14....8..0..8..0....8.10..8.10...11.13.11..9

Crossrefs

Column 1 is A001025

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

Row 1 is A188825(n+1)

Sequence in context: A223395 A202329 A223599 * A165115 A165117 A226966

Adjacent sequences: A223689 A223690 A223691 * A223693 A223694 A223695

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 25 2013

Status

approved