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%I #4 Mar 18 2013 21:16:17
%S 5,12,12,32,52,32,80,236,236,80,208,1076,2172,1076,208,528,4908,17828,
%T 17828,4908,528,1360,22388,166892,307144,166892,22388,1360,3472,
%U 102124,1382228,5359892,5359892,1382228,102124,3472,8912,465844,12894316
%N 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
%C Table starts
%C .....5......12.........32............80...............208..................528
%C ....12......52........236..........1076..............4908................22388
%C ....32.....236.......2172.........17828............166892..............1382228
%C ....80....1076......17828........307144...........5359892.............93770308
%C ...208....4908.....166892.......5359892.........200258884...........6581646956
%C ...528...22388....1382228......93770308........6581646956.........465277782336
%C ..1360..102124...12894316....1641741608......247417877452.......32969186423292
%C ..3472..465844..107283636...28748561780.....8146965446276.....2337308796813336
%C ..8912.2124972..996653548..503440061060...306270743418628...165726502883851820
%C .22800.9693172.8326150836.8816254627208.10089859264898796.11751198778793357708
%H R. H. Hardin, <a href="/A223255/b223255.txt">Table of n, a(n) for n = 1..312</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +4*a(n-2)
%F k=2: a(n) = 5*a(n-1) -2*a(n-2)
%F k=3: a(n) = 2*a(n-1) +75*a(n-2) -126*a(n-3) -70*a(n-4) +48*a(n-5)
%F 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
%F k=5: [order 16]
%F k=6: [order 24] for n>25
%F k=7: [order 59]
%e Some solutions for n=3 k=4
%e ..1..0..3..4....0..1..2..1....0..1..0..1....2..0..4..0....0..1..0..3
%e ..0..3..0..3....3..0..1..0....4..0..1..0....0..1..0..4....3..0..4..0
%e ..1..0..2..0....0..1..0..1....0..2..0..2....2..0..1..0....0..1..0..1
%Y Column 1 is A183682(n-1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Mar 18 2013