A223467 - OEIS

%I #4 Mar 20 2013 08:18:02

%S 21,60,60,190,400,190,600,2840,2840,600,1946,20588,47100,20588,1946,

%T 6264,150952,789796,789796,150952,6264,20440,1113460,13504044,

%U 31075684,13504044,1113460,20440,66208,8242836,231085748,1239353252,1239353252

%N T(n,k)=6X6X6 triangular graph without horizontal edges coloring a rectangular array: number of nXk 0..20 arrays where 0..20 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 3,6 3,7 4,7 4,8 5,8 5,9 6,10 6,11 7,11 7,12 8,12 8,13 9,13 9,14 10,15 10,16 11,16 11,17 12,17 12,18 13,18 13,19 14,19 14,20 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph

%C Table starts

%C .....21.........60............190................600..................1946

%C .....60........400...........2840..............20588................150952

%C ....190.......2840..........47100.............789796..............13504044

%C ....600......20588.........789796...........31075684............1239353252

%C ...1946.....150952.......13504044.........1239353252..........116111266332

%C ...6264....1113460......231085748........49754342824........10911947024556

%C ..20440....8242836.....3988872656......2005957755820......1033873786631384

%C ..66208...61154044....68744309868.....81082814719516.....97908623437928996

%C .216452..454323480..1190949680204...3283105035003140...9316198773171608432

%C .702768.3378142656.20584337901440.133083400954907428.885092803385071530352

%H R. H. Hardin, <a href="/A223467/b223467.txt">Table of n, a(n) for n = 1..180</a>

%e Some solutions for n=3 k=4

%e .11..6.11..7...10..6.10.16....1..0..2..0....1..0..2..4....1..3..7..3

%e ..7..3..7..4....6.11..6.10....4..1..4..2....0..1..0..1....3..1..3..1

%e ..4..1..3..7...11..7.11.16....2..0..2..5....1..4..2..4....7..3..1..4

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 20 2013