

A030077


Take n equally spaced points on circle, connect them by a path with n1 line segments; sequence gives number of distinct path lengths under action of dihedral group.


3



1, 1, 1, 3, 5, 17, 28, 105, 161, 670, 1001, 2869, 6188, 26565, 14502, 167898
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OFFSET

1,4


COMMENTS

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 n1 into floor(n/2) nonnegative parts, which is A099578(n2). It appears that the upper bound is attained for prime n. To find a(n), the length of A052558(n2) paths must be computed.  T. D. Noe, Jan 09 2007 [edited by Petros Hadjicostas, Jul 19 2018]


LINKS

Table of n, a(n) for n=1..16.


EXAMPLE

For n=4 the 3 lengths are: 3 boundary edges (length 3), edgediagonaledge (2 + sqrt(2)) and diagonaledgediagonal (1 + 2*sqrt(2)).
For n=5, the 4 edges of the path may include 0,...,4 diagonals, so a(5)=5.


CROSSREFS

Cf. A007874 (similar, but with n line segments).
Sequence in context: A032619 A193066 A193070 * A058580 A161682 A079373
Adjacent sequences: A030074 A030075 A030076 * A030078 A030079 A030080


KEYWORD

nonn,nice,more


AUTHOR

Daniel Lurie Gittelson


EXTENSIONS

More terms from T. D. Noe, Jan 09 2007


STATUS

approved



