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A223218 T(n,k)=3X3X3 triangular graph coloring a rectangular array: number of nXk 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

%I A223218 #6 Jul 23 2025 03:52:50
%S A223218 6,18,18,60,126,60,192,918,918,192,624,6642,15498,6642,624,2016,48114,
%T A223218 254694,254694,48114,2016,6528,348462,4232586,9640008,4232586,348462,
%U A223218 6528,21120,2523798,70014654,367156350,367156350,70014654,2523798,21120
%N A223218 T(n,k)=3X3X3 triangular graph coloring a rectangular array: number of nXk 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C A223218 Table starts
%C A223218 ......6........18............60...............192...................624
%C A223218 .....18.......126...........918..............6642.................48114
%C A223218 .....60.......918.........15498............254694...............4232586
%C A223218 ....192......6642........254694...........9640008.............367156350
%C A223218 ....624.....48114.......4232586.........367156350...........32213930742
%C A223218 ...2016....348462......70014654.......13964418774.........2819203560630
%C A223218 ...6528...2523798....1160465118......531419938920.......247143798101322
%C A223218 ..21120..18278946...19217863458....20220127602030.....21653415762483246
%C A223218 ..68352.132387858..318374151654...769404277676466...1897735773641654046
%C A223218 .221184.958837662.5273531868834.29276398278326448.166300121937966179310
%H A223218 R. H. Hardin, <a href="/A223218/b223218.txt">Table of n, a(n) for n = 1..220</a>
%F A223218 Empirical for column k:
%F A223218 k=1: a(n) = 2*a(n-1) +4*a(n-2)
%F A223218 k=2: a(n) = 6*a(n-1) +9*a(n-2)
%F A223218 k=3: [order 8]
%F A223218 k=4: [order 15]
%F A223218 k=5: [order 45]
%F A223218 k=6: [order 77]
%e A223218 Some solutions for n=3 k=4
%e A223218 ..0..1..0..1....0..1..2..5....4..3..1..2....0..2..1..4....0..1..4..1
%e A223218 ..1..4..1..4....1..2..5..4....3..4..2..1....1..4..2..1....1..0..1..4
%e A223218 ..2..1..2..5....4..1..4..5....4..3..1..4....0..2..1..2....4..2..4..5
%K A223218 nonn,tabl
%O A223218 1,1
%A A223218 _R. H. Hardin_ Mar 18 2013