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A223379 T(n,k)=3X3 square grid graph coloring a rectangular array: number of nXk 0..8 arrays where 0..8 label nodes of the square grid graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph 9
9, 24, 24, 68, 144, 68, 192, 912, 912, 192, 544, 5808, 13232, 5808, 544, 1536, 37008, 192752, 192752, 37008, 1536, 4352, 235824, 2812608, 6443888, 2812608, 235824, 4352, 12288, 1502736, 41044048, 215773456, 215773456, 41044048, 1502736, 12288 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

.....9........24............68..............192..................544

....24.......144...........912.............5808................37008

....68.......912.........13232...........192752..............2812608

...192......5808........192752..........6443888............215773456

...544.....37008.......2812608........215773456..........16589428016

..1536....235824......41044048.......7226963248........1275808315376

..4352...1502736.....598980512.....242067684912.......98124582178928

.12288...9575856....8741293936....8108163611488.....7547020636487088

.34816..61020048..127567402912..271587161033712...580464274863214064

.98304.388836912.1861673117136.9096958174072272.44645287470831363696

LINKS

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

FORMULA

Empirical for column k:

k=1: a(n) = 8*a(n-2) for n>3

k=2: a(n) = 7*a(n-1) -4*a(n-2)

k=3: a(n) = 221*a(n-2) -1718*a(n-4) +1872*a(n-6) for n>7

k=4: [order 9]

k=5: [order 28] for n>29

k=6: [order 59]

EXAMPLE

Some solutions for n=3 k=4

..0..1..4..5....5..4..7..6....1..4..5..4....4..7..4..7....2..1..2..1

..1..4..5..4....2..5..8..7....4..1..4..5....3..6..3..6....5..2..5..2

..2..1..2..5....1..4..5..8....7..4..7..4....6..3..4..7....8..5..2..5

Vertex neighbors:

0 -> 1 3

1 -> 0 2 4

2 -> 1 5

3 -> 0 4 6

4 -> 3 1 5 7

5 -> 4 2 8

6 -> 3 7

7 -> 6 4 8

8 -> 7 5

CROSSREFS

Sequence in context: A247960 A347559 A161431 * A223297 A317493 A102217

Adjacent sequences:  A223376 A223377 A223378 * A223380 A223381 A223382

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 19 2013

STATUS

approved

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Last modified January 29 05:09 EST 2022. Contains 350672 sequences. (Running on oeis4.)