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A093128
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Number of dissections of a polygon using strictly disjoint diagonals.
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1
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1, 1, 3, 6, 13, 29, 65, 148, 341, 793, 1860, 4395, 10452, 24999, 60097, 145130, 351916, 856502, 2091599, 5123437, 12585354, 30995031, 76516348, 189310421, 469335998, 1165790119
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) = number of dissections of a regular (n+2)-gon using 0 or more strictly disjoint diagonals. a(n) = A004148(n+2)-A004148(n) for n>=1. Row sums of A093127.
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FORMULA
| G.f.: 1+(1+x)(1 - 2x - x^3 - ((1 -3*x+ x^2)(1-x)(1-x^3))^(1/2) )/(2*x^4).
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EXAMPLE
| a(3)=6 because there are 5 ways to insert a single diagonal into a
pentagon plus the empty dissection
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CROSSREFS
| Sequence in context: A071014 A078061 A018909 * A005313 A108639 A087218
Adjacent sequences: A093125 A093126 A093127 * A093129 A093130 A093131
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KEYWORD
| easy,nonn
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AUTHOR
| David Callan (callan(AT)stat.wisc.edu), Mar 23 2004
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