A223379 - OEIS

%I #4 Mar 19 2013 17:12:52

%S 9,24,24,68,144,68,192,912,912,192,544,5808,13232,5808,544,1536,37008,

%T 192752,192752,37008,1536,4352,235824,2812608,6443888,2812608,235824,

%U 4352,12288,1502736,41044048,215773456,215773456,41044048,1502736,12288

%N 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

%C Table starts

%C .....9........24............68..............192..................544

%C ....24.......144...........912.............5808................37008

%C ....68.......912.........13232...........192752..............2812608

%C ...192......5808........192752..........6443888............215773456

%C ...544.....37008.......2812608........215773456..........16589428016

%C ..1536....235824......41044048.......7226963248........1275808315376

%C ..4352...1502736.....598980512.....242067684912.......98124582178928

%C .12288...9575856....8741293936....8108163611488.....7547020636487088

%C .34816..61020048..127567402912..271587161033712...580464274863214064

%C .98304.388836912.1861673117136.9096958174072272.44645287470831363696

%H R. H. Hardin, <a href="/A223379/b223379.txt">Table of n, a(n) for n = 1..264</a>

%F Empirical for column k:

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

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

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

%F k=4: [order 9]

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

%F k=6: [order 59]

%e Some solutions for n=3 k=4

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

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

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

%e Vertex neighbors:

%e 0 -> 1 3

%e 1 -> 0 2 4

%e 2 -> 1 5

%e 3 -> 0 4 6

%e 4 -> 3 1 5 7

%e 5 -> 4 2 8

%e 6 -> 3 7

%e 7 -> 6 4 8

%e 8 -> 7 5

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 19 2013