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, 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

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