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Search: id:A054514
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| A054514 |
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Number of ways to place non-crossing diagonals in convex (n+4)-gon so as to create no triangles or quadrilaterals. |
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+0
2
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| 1, 1, 1, 5, 10, 16, 45, 109, 222, 540, 1341, 3065, 7328, 18112, 43530, 105390, 260254, 639244, 1570257, 3893805, 9669236
(list; graph; listen)
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OFFSET
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1,4
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LINKS
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L. Smiley, Generalization and some variants
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FORMULA
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a(n) = Sum_{j=0..(n-1)/3} binomial[n-2j-1, n-3j-1] binomial[n+3+j, n+2]/(n+3). This counts the polygon dissections above by number j of diagonals. - David Callan (callan(AT)stat.wisc.edu), Jul 15 2004
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EXAMPLE
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a(4)=5 because the octagon has the null placement and four ways to place a single diagonal.
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MATHEMATICA
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InverseSeries[Series[(y-y^2-y^4)/(1-y), {y, 0, 24}], x] (* then A(x)=[y(x)-x]/x^3 *)
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CROSSREFS
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A046736, A049124, A003168, A054515.
Sequence in context: A052905 A026059 A115002 this_sequence A002660 A050321 A083866
Adjacent sequences: A054511 A054512 A054513 this_sequence A054515 A054516 A054517
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KEYWORD
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nonn
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AUTHOR
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Len Smiley (smiley(AT)math.uaa.alaska.edu), Apr 08 2000
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