A223415 T(n,k)=4X4X4 triangular graph without horizontal edges coloring a rectangular array: number of nXk 0..9 arrays where 0..9 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 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph

10, 24, 24, 66, 132, 66, 176, 780, 780, 176, 486, 4664, 10496, 4664, 486, 1312, 28060, 139552, 139552, 28060, 1312, 3622, 169124, 1905248, 4222748, 1905248, 169124, 3622, 9792, 1020056, 25615364, 128885376, 128885376, 25615364, 1020056, 9792

Offset

1,1

Comments

Table starts

....10........24...........66..............176..................486

....24.......132..........780.............4664................28060

....66.......780........10496...........139552..............1905248

...176......4664.......139552..........4222748............128885376

...486.....28060......1905248........128885376...........8949958604

..1312....169124.....25615364.......3940419696.........612911291636

..3622...1020056....350374768.....120598735372.......42673331495196

..9792...6153860...4718334196....3692032452520.....2927250803834708

.27030..37128748..64553618848..113045815121672...203882215723328784

.73088.224020376.869537910656.3461502762735476.13989519933873595328

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

k=1: a(n) = 9*a(n-2) -12*a(n-4) +4*a(n-6)

k=2: a(n) = 9*a(n-1) -17*a(n-2) -10*a(n-3) +26*a(n-4) +10*a(n-5)

k=3: [order 18] for n>19

k=4: [order 31]

k=5: [order 96] for n>97

Example

Some solutions for n=3 k=4
..0..1..3..7....1..3..7..4....2..4..7..3....2..4..1..4....7..3..6..3
..1..4..1..4....0..1..3..7....4..7..3..1....4..2..4..8....3..6..3..6
..4..2..0..1....2..4..1..4....7..4..1..3....8..5..8..4....1..3..1..3

Crossrefs

Sequence in context: A102089 A250797 A250583 * A187629 A175403 A133503

Adjacent sequences: A223412 A223413 A223414 * A223416 A223417 A223418

Keyword

nonn,tabl

Author

R. H. Hardin Mar 20 2013

Status

approved