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%I #4 Mar 19 2013 18:17:39
%S 16,48,48,152,328,152,488,2360,2360,488,1576,17280,39480,17280,1576,
%T 5096,127464,672784,672784,127464,5096,16488,943016,11561512,26836512,
%U 11561512,943016,16488,53352,6985008,199425400,1080643264,1080643264
%N T(n,k)=4X4 square grid graph coloring a rectangular array: number of nXk 0..15 arrays where 0..15 label nodes of the square grid graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph
%C Table starts
%C .....16.........48............152................488..................1576
%C .....48........328...........2360..............17280................127464
%C ....152.......2360..........39480.............672784..............11561512
%C ....488......17280.........672784...........26836512............1080643264
%C ...1576.....127464.......11561512.........1080643264..........102163935000
%C ...5096.....943016......199425400........43699580872.........9705525235832
%C ..16488....6985008.....3445747472......1770698081072.......924127826390176
%C ..53352...51763176....59582558136.....71817607508112.....88090590750261080
%C .172648..383669400..1030635314552...2914205675816528...8401742793556003144
%C .558696.2843977792.17830297764560.118279017948229984.801551619655700687184
%H R. H. Hardin, <a href="/A223402/b223402.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1) +2*a(n-2) -4*a(n-3)
%F k=2: a(n) = 10*a(n-1) -18*a(n-2) -9*a(n-3) +2*a(n-4)
%F k=3: [order 12] for n>13
%F k=4: [order 28] for n>29
%F k=5: [order 94] for n>95
%e Some solutions for n=3 k=4
%e ..4..8..9..5....5..6..2..1....0..1..5..4....8..4..5..6....1..0..1..5
%e ..8..4..5..4....4..5..1..0....4..5..6..5....4..5..1..5....0..1..5..6
%e .12..8..9..8....0..4..5..1....8..9..5..9....8..9..5..6....1..5..4..5
%e Vertex neighbors:
%e 0 -> 1 4
%e 1 -> 0 2 5
%e 2 -> 1 3 6
%e 3 -> 2 7
%e 4 -> 0 5 8
%e 5 -> 4 1 6 9
%e 6 -> 5 2 7 10
%e 7 -> 6 3 11
%e 8 -> 4 9 12
%e 9 -> 8 5 10 13
%e 10 -> 9 6 11 14
%e 11 -> 10 7 15
%e 12 -> 8 13
%e 13 -> 12 9 14
%e 14 -> 13 10 15
%e 15 -> 14 11
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Mar 19 2013
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