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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 9
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 22 03:20 EDT 2021. Contains 347605 sequences. (Running on oeis4.)