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

1,1

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

Links

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

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]

Example

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

Crossrefs

Column 2 is A223249

Sequence in context: A298016 A055595 A132632 * A063648 A331209 A063722

Adjacent sequences: A223349 A223350 A223351 * A223353 A223354 A223355

Keyword

nonn,tabl

Author

R. H. Hardin Mar 19 2013

Status

approved