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A007569
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Number of nodes in regular n-gon with all diagonals drawn.
(Formerly M0724)
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11
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1, 2, 3, 5, 10, 19, 42, 57, 135, 171, 341, 313, 728, 771, 1380, 1393, 2397, 1855, 3895, 3861, 6006, 5963, 8878, 7321, 12675, 12507, 17577, 17277, 23780, 16831, 31496, 30945, 40953, 40291, 52395, 47017, 66082, 65019, 82290
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Sascha Kurz, m-gons in regular n-gons
B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.
B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, SIAM J. on Discrete Mathematics, Vol. 11, No. 1, 135-156 (1998).
B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, arXiv version, which has fewer typos than the SIAM version.
B. Poonen and M. Rubinstein, Mathematica programs for these sequences
Sequences formed by drawing all diagonals in regular polygon
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FORMULA
| a(n)=A006561(n)+n. - T. D. Noe, Dec 23 2006
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MATHEMATICA
| del[m_, n_]:=If[Mod[n, m]==0, 1, 0]; Int[n_]:=If[n<4, n, n + Binomial[n, 4] + del[2, n](-5n^3+45n^2-70n+24)/24 - del[4, n](3n/2) + del[6, n](-45n^2+262n)/6 + del[12, n]*42n + del[18, n]*60n + del[24, n]*35n - del[30, n]*38n - del[42, n]*82n - del[60, n]*330n - del[84, n]*144n - del[90, n]*96n - del[120, n]*144n - del[210, n]*96n]; Table[Int[n], {n, 1, 1000}] - T. D. Noe (noe(AT)sspectra.com), Dec 21 2006
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CROSSREFS
| Sequences related to chords in a circle: A001006, A054726, A006533, A006561, A006600, A007569, A007678. See also entries for chord diagrams in Index file.
Sequence in context: A046630 A177874 A064236 * A054317 A065840 A093785
Adjacent sequences: A007566 A007567 A007568 * A007570 A007571 A007572
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KEYWORD
| easy,nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Bjorn Poonen (poonen(AT)math.princeton.edu)
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