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Search: id:A087809
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| A087809 |
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Number of triangulations (by Euclidean triangles) having 3+3n vertices of a triangle with each side subdivided by n additional points. |
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+0
1
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| 1, 4, 29, 229, 1847, 14974, 121430, 983476, 7952111, 64193728, 517447289, 4165721377, 33500374796, 269166095800, 2161064409680, 17339917293304, 139060729285871, 1114752741216196, 8933074352513183, 71564554425680839
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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R. Bacher, Counting Triangulations of Configurations, arXiv:math.CO/0310206, http://fr.arXiv.org/abs/math.CO/0310206
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FORMULA
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A formula is given in the reference below.
It seems that a(n)=sum_{i, j, k>=0}C(n, i+j)*C(n, j+k)*C(n, k+i)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 25 2004
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EXAMPLE
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a(0)=1 since there is only one triangulation of a triangle (consisting of the triangle itself).
The a(1)=4 triangulations of a triangle with each side subdivided by one additional point are given by
......O............O
...../.\........../|\
....O._.O........O...O
.../.\./.\..,.../.\|/.\
..O._.O._.O....O._.O._.O
and rotations by 120 degrees and 240 degrees of the last triangulation.
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CROSSREFS
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Sequence in context: A001883 A135429 A079756 this_sequence A140526 A151343 A125808
Adjacent sequences: A087806 A087807 A087808 this_sequence A087810 A087811 A087812
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KEYWORD
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nonn,nice
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AUTHOR
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Roland Bacher (roland.bacher(AT)ujf-grenoble.fr), Oct 16 2003
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