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Search: id:A035029
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| A035029 |
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Sum{k=0..n, (k+1) * Sum[l=0..n, 2^l*C(n,l)*C(n-k,l) ]}. |
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+0
3
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| 1, 5, 26, 138, 743, 4043, 22180, 122468, 679757, 3789297, 21199998, 118973550, 669447123, 3775577367, 21336790152, 120795829128, 684962855705, 3889578815453, 22115533878178, 125892252068498, 717400693313471
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Number of regions in all the dissections of a convex (n+3)-gon by non-intersecting diagonals. a(1)=5 because in the three dissections of a square we have alltogether five regions: one in the "no-diagonals" dissection and two in each of the dissections by one of the two diagonals of the square. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 28 2003
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LINKS
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Milan Janjic, Two Enumerative Functions
D. Merlini, R. Sprugnoli and M. C. Verri, Waiting patterns for a printer, FUN with algorithm'01, Isola d'Elba, 2001.
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FORMULA
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G.f.=(1-z)^2/[8z^2sqrt(1-6*z+z^2)]-(1+z)/(8z^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 28 2003
a(n) = T(n+1, n+2), array T as in A049600.
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CROSSREFS
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Equals (1/4) [A002002(n+1) - A002002(n)].
Cf. A001003.
Sequence in context: A076025 A161731 A049607 this_sequence A081569 A005573 A081911
Adjacent sequences: A035026 A035027 A035028 this_sequence A035030 A035031 A035032
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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