A223255 T(n,k)=Two-loop graph coloring a rectangular array: number of nXk 0..4 arrays where 0..4 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
5, 12, 12, 32, 52, 32, 80, 236, 236, 80, 208, 1076, 2172, 1076, 208, 528, 4908, 17828, 17828, 4908, 528, 1360, 22388, 166892, 307144, 166892, 22388, 1360, 3472, 102124, 1382228, 5359892, 5359892, 1382228, 102124, 3472, 8912, 465844, 12894316
Offset: 1
Examples
Some solutions for n=3 k=4 ..1..0..3..4....0..1..2..1....0..1..0..1....2..0..4..0....0..1..0..3 ..0..3..0..3....3..0..1..0....4..0..1..0....0..1..0..4....3..0..4..0 ..1..0..2..0....0..1..0..1....0..2..0..2....2..0..1..0....0..1..0..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..312
Crossrefs
Column 1 is A183682(n-1)
Formula
Empirical for column k:
k=1: a(n) = a(n-1) +4*a(n-2)
k=2: a(n) = 5*a(n-1) -2*a(n-2)
k=3: a(n) = 2*a(n-1) +75*a(n-2) -126*a(n-3) -70*a(n-4) +48*a(n-5)
k=4: a(n) = 20*a(n-1) -28*a(n-2) -299*a(n-3) +436*a(n-4) +476*a(n-5) -460*a(n-6) for n>7
k=5: [order 16]
k=6: [order 24] for n>25
k=7: [order 59]
Comments