A223245 - OEIS

%I #4 Mar 18 2013 20:53:50

%S 1536,165894,33590454,7399451382,1657797796530,372027916726176,

%T 83513173388559498,18747680181924131604,4208647623258085653138,

%U 944795541265761949037394,212096328321250798503916836

%N 3-loop graph coloring a rectangular array: number of nX6 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 0,5 5,6 6,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph

%C Column 6 of A223247

%H R. H. Hardin, <a href="/A223245/b223245.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 243*a(n-1) -3105*a(n-2) -256456*a(n-3) +4509365*a(n-4) +31260277*a(n-5) -850062930*a(n-6) +562462962*a(n-7) +52286136004*a(n-8) -171853669310*a(n-9) -1146926517433*a(n-10) +5722298474311*a(n-11) +8026339261153*a(n-12) -71375095891923*a(n-13) +17744778171571*a(n-14) +379900399928432*a(n-15) -386615281004556*a(n-16) -812176772051396*a(n-17) +1318606323540448*a(n-18) +370513469882640*a(n-19) -1404472060621520*a(n-20) +388809009769216*a(n-21) +307181922411008*a(n-22) -114706766807040*a(n-23) -6532481536000*a(n-24) for n>25

%e Some solutions for n=3

%e ..3..0..1..0..2..1....3..0..1..0..1..0....3..0..1..0..4..3....3..0..3..0..6..0

%e ..0..3..0..2..0..2....0..5..0..4..0..6....0..3..0..3..0..4....0..3..0..4..0..4

%e ..3..0..5..0..4..0....3..0..5..0..1..0....3..0..5..0..6..0....3..0..2..0..2..0

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 18 2013