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A030077 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. 3
1, 1, 1, 3, 5, 17, 28, 105, 161, 670, 1001, 2869, 6188, 26565, 14502, 167898 (list; graph; refs; listen; history; text; internal format)
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 n-1 into floor(n/2) nonnegative 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, 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), edge-diagonal-edge (2 + sqrt(2)) and diagonal-edge-diagonal (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

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Last modified January 26 11:22 EST 2022. Contains 350598 sequences. (Running on oeis4.)