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Search: id:A030077
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| A030077 |
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Take n equally spaced points on circle, connect them by a path with n-1 line segments; sequence gives number of distinct path lengths under action of dihedral group. |
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+0
4
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| 1, 1, 1, 3, 5, 17, 28, 105, 161, 670, 1001, 2869, 6188, 26565, 14502, 167898
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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For n points on a circle, there are floor(n/2) distinct line segment lengths. Hence an upper bound for a(n) is the number of compositions of n-1 into floor(n/2) parts, which is A099578(n-2). It appears that the upper bound is attained for prime n. To find a(n), the length of A052558(n-2) paths must be computed. - T. D. Noe (noe(AT)sspectra.com), Jan 09 2007
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EXAMPLE
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For n=4 the 3 lengths are: 3 boundary edges (length 3), edge-diagonal-edge (2 + sqrt 2) and diagonal-edge-diagonal (1 + 2sqrt 2). For n=5, the 4 edges of the path may include 0,...,4 diagonals, so a(5)=5.
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CROSSREFS
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Cf. A007874 (similar, but with n line segments).
Sequence in context: A024867 A025111 A032619 this_sequence A058580 A161682 A079373
Adjacent sequences: A030074 A030075 A030076 this_sequence A030078 A030079 A030080
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KEYWORD
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nonn,nice,more
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AUTHOR
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Daniel Gittelson (danielgittelson(AT)hotmail.com)
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Jan 09 2007
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