A223344 T(n,k)=5X5X5 triangular graph coloring a rectangular array: number of nXk 0..14 arrays where 0..14 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 3,6 3,7 4,7 6,7 4,8 5,8 7,8 5,9 8,9 6,10 6,11 7,11 10,11 7,12 8,12 11,12 11,12 8,13 9,13 12,13 9,14 13,14 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph

15, 60, 60, 264, 612, 264, 1176, 6696, 6696, 1176, 5280, 74736, 190740, 74736, 5280, 23712, 840456, 5514360, 5514360, 840456, 23712, 106560, 9474840, 161370036, 419434596, 161370036, 9474840, 106560, 478848, 106904016, 4730218284

Offset

1,1

Comments

Table starts

......15...........60..............264.................1176

......60..........612.............6696................74736

.....264.........6696...........190740..............5514360

....1176........74736..........5514360............419434596

....5280.......840456........161370036..........32292951660

...23712......9474840.......4730218284........2496237714588

..106560....106904016.....138947808456......193291992449808

..478848...1206530100....4081817304888....14976739459479096

.2151936..13618313028..119957730775764..1160751100183303776

.9670656.153717108696.3525232400391672.89971810635836546940

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) +4*a(n-2) -8*a(n-3)

k=2: a(n) = 13*a(n-1) -11*a(n-2) -94*a(n-3) -7*a(n-4) +79*a(n-5) -3*a(n-6)

k=3: [order 30]

Example

Some solutions for n=3 k=4
..7..3..7..4....7.11..6..3....7..4..5..4....7..3..7..8....7..3..7..3
..3..1..4..7....3..6.11..7....3..7..4..1....3..4..8..4....3..1..3..7
..1..4..7..8....1..3..7.11....7..4..1..0....4..8..9..8....6..3..4..8

Crossrefs

Sequence in context: A261798 A022287 A288747 * A206238 A064761 A005945

Adjacent sequences: A223341 A223342 A223343 * A223345 A223346 A223347

Keyword

nonn,tabl

Author

R. H. Hardin Mar 19 2013

Status

approved