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A089382
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Total number of triangles in all the dissections of a convex (n+3)-gon by nonintersecting diagonals.
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0
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1, 4, 20, 104, 553, 2984, 16272, 89440, 494681, 2749772, 15348372, 85967112, 482927985, 2719787856, 15351385152, 86816721792, 491819758417, 2790451952660, 15854070902964, 90187514559208, 513619224125657
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: (3-z+q)(1+z-q)^2/(64qz^2), where q = sqrt(1-6z+z^2).
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EXAMPLE
| a(1)=4 because in the three dissections of a square we have alltogether four triangles: no triangle in the "no-diagonals" dissection and two triangles in each of the dissections by one of the two diagonals of the square.
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CROSSREFS
| Cf. A001003.
Sequence in context: A120978 A104550 A035028 * A192619 A026305 A195256
Adjacent sequences: A089379 A089380 A089381 * A089383 A089384 A089385
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 28 2003
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