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A105638
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Maximum number of intersections in self-intersecting n-gon.
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3
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0, 1, 5, 7, 14, 17, 27, 31, 44, 49, 65, 71, 90, 97, 119, 127, 152, 161, 189, 199, 230, 241, 275, 287, 324, 337, 377, 391, 434, 449, 495, 511, 560, 577, 629, 647, 702, 721, 779, 799, 860, 881, 945, 967, 1034, 1057, 1127, 1151, 1224, 1249, 1325, 1351, 1430, 1457
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,3
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REFERENCES
| B. Gruenbaum, Selfintersections of Polygons, Geombinatorics, Volume VIII 4(1998), pp. 37-45.
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LINKS
| David W. Wilson, Table of n, a(n) for n=3..10000
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FORMULA
| a(n) = n(n-3)/2 if n odd, n(n-4)/2+1 if n even.
a(n) = a(n-1) + 2a(n-2) - 2a(n-3) - a(n-4) + a(n-5)
G.f.: x^4*(1+4*x-x^3)/(1-x-2*x^2+2*x^3+x^4-x^5). [Colin Barker, Jan 31 2012]
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EXAMPLE
| The self-intersecting pentagon with the largest number of intersections is the star polygon {5/2} (pentacle}, with 5 intersections, hence a(5) = 5.
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CROSSREFS
| Sequence in context: A158892 A106022 A050085 * A030795 A043099 A030755
Adjacent sequences: A105635 A105636 A105637 * A105639 A105640 A105641
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KEYWORD
| nonn,easy
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net), Apr 16 2005
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