A223467 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

21, 60, 60, 190, 400, 190, 600, 2840, 2840, 600, 1946, 20588, 47100, 20588, 1946, 6264, 150952, 789796, 789796, 150952, 6264, 20440, 1113460, 13504044, 31075684, 13504044, 1113460, 20440, 66208, 8242836, 231085748, 1239353252, 1239353252

Offset

1,1

Comments

Table starts

.....21.........60............190................600..................1946

.....60........400...........2840..............20588................150952

....190.......2840..........47100.............789796..............13504044

....600......20588.........789796...........31075684............1239353252

...1946.....150952.......13504044.........1239353252..........116111266332

...6264....1113460......231085748........49754342824........10911947024556

..20440....8242836.....3988872656......2005957755820......1033873786631384

..66208...61154044....68744309868.....81082814719516.....97908623437928996

.216452..454323480..1190949680204...3283105035003140...9316198773171608432

.702768.3378142656.20584337901440.133083400954907428.885092803385071530352

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Example

Some solutions for n=3 k=4
.11..6.11..7...10..6.10.16....1..0..2..0....1..0..2..4....1..3..7..3
..7..3..7..4....6.11..6.10....4..1..4..2....0..1..0..1....3..1..3..1
..4..1..3..7...11..7.11.16....2..0..2..5....1..4..2..4....7..3..1..4

Crossrefs

Sequence in context: A370519 A037305 A370109 * A051873 A223460 A219690

Adjacent sequences: A223464 A223465 A223466 * A223468 A223469 A223470

Keyword

nonn,tabl

Author

R. H. Hardin Mar 20 2013

Status

approved