A007874 Distinct perimeter lengths of polygons with regularly spaced vertices.

1, 1, 1, 2, 4, 10, 24, 63, 177, 428, 1230, 2556, 8202, 18506, 18162, 119069

Offset: 1

Author

Peter H. Borcherds (p.h.borcherds(AT)bham.ac.uk)

Keywords

• nonn

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 into floor(n/2) nonnegative parts, which is A127040(n-2). To find a(n), the length of A052558(n-2) paths must be computed. - T. D. Noe, Jan 13 2007 [edited by Petros Hadjicostas, Jul 19 2018]

Examples

			Consider n=4. Label the points on the circle A,B,C and D. Suppose that AB has unit length. Then a(4)=2 because the two 4-gons are ABCDA and ACBDA, with perimeters 4 and 2+2*sqrt(2), respectively.
		

Crossrefs

Cf. A030077.

Extensions

More terms from T. D. Noe, Jan 13 2007