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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
15, 40, 40, 120, 248, 120, 356, 1648, 1648, 356, 1088, 11168, 25436, 11168, 1088, 3276, 76384, 394736, 394736, 76384, 3276, 10052, 524736, 6256832, 14270468, 6256832, 524736, 10052, 30380, 3613024, 98783592, 522011152, 522011152, 98783592 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Table starts
.....15.........40...........120...............356..................1088
.....40........248..........1648.............11168.................76384
....120.......1648.........25436............394736...............6256832
....356......11168........394736..........14270468.............522011152
...1088......76384.......6256832.........522011152...........44494633876
...3276.....524736......98783592.......19187276496.........3786278496752
..10052....3613024....1575629948......707293805988.......325249041493488
..30380...24906592...24993296408....26110271476744.....27818291732538560
..93296..171802144..399339124688...964706306602248...2394866308625232348
.282240.1185459328.6343618034616.35659725052665944.205161525882369203816
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 14*a(n-2) -49*a(n-4) +49*a(n-6) for n>7
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)
k=3: [order 32] for n>33
k=4: [order 71]
EXAMPLE
Some solutions for n=3 k=4
.11..7..4..7....7..4..7..4....7..4..8.12...11..7..4..1...11..7.11..7
..7.12..7.12....4..1..4..1....3..1..4..7....7..3..7..3....7.12..7.12
..4..7..4..8....1..0..2..4....6..3..7..3....4..1..4..7...12..7.12..8
CROSSREFS
Sequence in context: A369720 A369758 A325659 * A044092 A044473 A321491
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 20 2013
STATUS
approved

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Last modified May 21 13:44 EDT 2024. Contains 372738 sequences. (Running on oeis4.)