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Search: id:A007874
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| A007874 |
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Distinct perimeter lengths of polygons with regularly spaced vertices. |
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+0
3
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| 1, 1, 1, 2, 4, 10, 24, 63, 177, 428, 1230, 2556, 8202, 18506, 18162, 119069
(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 into floor(n/2) parts, which is A127040(n-2). To find a(n), the length of A052558(n-2) paths must be computed. - T. D. Noe (noe(AT)sspectra.com), Jan 13 2007
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EXAMPLE
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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.
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CROSSREFS
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Cf. A030077.
Adjacent sequences: A007871 A007872 A007873 this_sequence A007875 A007876 A007877
Sequence in context: A121691 A124499 A132220 this_sequence A121704 A049144 A049131
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KEYWORD
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nonn
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AUTHOR
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Peter H. Borcherds p.h.borcherds(AT)bham.ac.uk
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Jan 13 2007
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