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A223432 T(n,k)=5X5X5 triangular graph without horizontal edges coloring a rectangular array: number of nXk 0..14 arrays where 0..14 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 6,10 6,11 7,11 7,12 8,12 8,13 9,13 9,14 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph 9

%I #4 Mar 20 2013 05:48:57

%S 15,40,40,120,248,120,356,1648,1648,356,1088,11168,25436,11168,1088,

%T 3276,76384,394736,394736,76384,3276,10052,524736,6256832,14270468,

%U 6256832,524736,10052,30380,3613024,98783592,522011152,522011152,98783592

%N T(n,k)=5X5X5 triangular graph without horizontal edges coloring a rectangular array: number of nXk 0..14 arrays where 0..14 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 6,10 6,11 7,11 7,12 8,12 8,13 9,13 9,14 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph

%C Table starts

%C .....15.........40...........120...............356..................1088

%C .....40........248..........1648.............11168.................76384

%C ....120.......1648.........25436............394736...............6256832

%C ....356......11168........394736..........14270468.............522011152

%C ...1088......76384.......6256832.........522011152...........44494633876

%C ...3276.....524736......98783592.......19187276496.........3786278496752

%C ..10052....3613024....1575629948......707293805988.......325249041493488

%C ..30380...24906592...24993296408....26110271476744.....27818291732538560

%C ..93296..171802144..399339124688...964706306602248...2394866308625232348

%C .282240.1185459328.6343618034616.35659725052665944.205161525882369203816

%H R. H. Hardin, <a href="/A223432/b223432.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

%F k=1: a(n) = 14*a(n-2) -49*a(n-4) +49*a(n-6) for n>7

%F k=2: a(n) = 14*a(n-1) -57*a(n-2) +28*a(n-3) +225*a(n-4) -230*a(n-5) -192*a(n-6) +232*a(n-7) +28*a(n-8) -48*a(n-9)

%F k=3: [order 32] for n>33

%F k=4: [order 71]

%e Some solutions for n=3 k=4

%e .11..7..4..7....7..4..7..4....7..4..8.12...11..7..4..1...11..7.11..7

%e ..7.12..7.12....4..1..4..1....3..1..4..7....7..3..7..3....7.12..7.12

%e ..4..7..4..8....1..0..2..4....6..3..7..3....4..1..4..7...12..7.12..8

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 20 2013

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Last modified June 13 05:35 EDT 2024. Contains 373366 sequences. (Running on oeis4.)