A223352 T(n,k)=3X3X3 triangular graph without horizontal edges coloring a rectangular array: number of nXk 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

6, 12, 12, 28, 52, 28, 60, 236, 236, 60, 140, 1076, 2280, 1076, 140, 300, 4908, 20836, 20836, 4908, 300, 700, 22388, 202264, 405988, 202264, 22388, 700, 1500, 102124, 1851020, 7918948, 7918948, 1851020, 102124, 1500, 3500, 465844, 17970056

Offset: 1

Author

R. H. Hardin Mar 19 2013

Keywords

• nonn
• tabl

Comments

Table starts

....6......12..........28.............60...............140..................300

...12......52.........236...........1076..............4908................22388

...28.....236........2280..........20836............202264..............1851020

...60....1076.......20836.........405988...........7918948............154482340

..140....4908......202264........7918948.........329268616..........12912752876

..300...22388.....1851020......154482340.......12912752876........1079538816324

..700..102124....17970056.....3013692516......537001573656.......90254934876620

.1500..465844...164457412....58792282660....21060038730884.....7545802995190884

.3500.2124972..1596586328..1146943179236...875825392204488...630870570544801836

.7500.9693172.14611562156.22375024222628.34348003384801484.52744249735952687492

Examples

			Some solutions for n=3 k=4
..1..0..1..4....1..0..1..4....2..0..1..0....3..1..0..1....4..1..0..2
..4..2..4..2....3..1..0..2....4..1..0..2....1..3..1..0....1..0..2..4
..1..0..1..4....1..4..2..0....2..4..2..4....0..1..0..2....4..2..4..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..480

Crossrefs

Column 2 is A223249

Formula

Empirical for column k:

k=1: a(n) = 5*a(n-2) for n>3

k=2: a(n) = 5*a(n-1) -2*a(n-2)

k=3: a(n) = 91*a(n-2) -192*a(n-4) +64*a(n-6)

k=4: a(n) = 23*a(n-1) -66*a(n-2) -52*a(n-3) +208*a(n-4) +32*a(n-5) -128*a(n-6)

k=5: [order 12] for n>13

k=6: [order 18]

k=7: [order 36]