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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

%I

%S 10,24,24,66,132,66,176,780,780,176,486,4664,10496,4664,486,1312,

%T 28060,139552,139552,28060,1312,3622,169124,1905248,4222748,1905248,

%U 169124,3622,9792,1020056,25615364,128885376,128885376,25615364,1020056,9792

%N 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

%C Table starts

%C ....10........24...........66..............176..................486

%C ....24.......132..........780.............4664................28060

%C ....66.......780........10496...........139552..............1905248

%C ...176......4664.......139552..........4222748............128885376

%C ...486.....28060......1905248........128885376...........8949958604

%C ..1312....169124.....25615364.......3940419696.........612911291636

%C ..3622...1020056....350374768.....120598735372.......42673331495196

%C ..9792...6153860...4718334196....3692032452520.....2927250803834708

%C .27030..37128748..64553618848..113045815121672...203882215723328784

%C .73088.224020376.869537910656.3461502762735476.13989519933873595328

%H R. H. Hardin, <a href="/A223415/b223415.txt">Table of n, a(n) for n = 1..264</a>

%F Empirical for column k:

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

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

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

%F k=4: [order 31]

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

%e Some solutions for n=3 k=4

%e ..0..1..3..7....1..3..7..4....2..4..7..3....2..4..1..4....7..3..6..3

%e ..1..4..1..4....0..1..3..7....4..7..3..1....4..2..4..8....3..6..3..6

%e ..4..2..0..1....2..4..1..4....7..4..1..3....8..5..8..4....1..3..1..3

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 20 2013

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Last modified October 20 04:52 EDT 2021. Contains 348099 sequences. (Running on oeis4.)