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A115178
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Expansion of c(x^2+x^3), c(x) the g.f. of A000108.
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3
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1, 0, 1, 1, 2, 4, 7, 15, 29, 61, 126, 266, 566, 1212, 2619, 5685, 12419, 27247, 60049, 132847, 294931, 656877, 1467258, 3286218, 7378240, 16603458, 37441990, 84599854, 191501532, 434224404, 986161959, 2243009869, 5108859821
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Diagonal sums of number triangle A117434.
a(n) = number of Motzkin n-paths (A001006) in which every flatstep (F) is followed by a downstep (D). For example, a(5)=4 counts UDUFD, UFDUD, UUDFD, UUFDD. - David Callan (callan(AT)stat.wisc.edu), Jun 07 2006
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FORMULA
| a(n)=sum{k=0..floor(n/2), C(k)C(k,n-2k)}.
Conjecture: (n+2)*a(n) +(n+2)*a(n-1) +4*(1-n)*a(n-2) +2*(7-4*n)*a(n-3) +2*(5-2*n)*a(n-4)=0. - R. J. Mathar, Nov 15 2011
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CROSSREFS
| Cf. A007477.
Sequence in context: A171276 A027167 A136336 * A049885 A129682 A129981
Adjacent sequences: A115175 A115176 A115177 * A115179 A115180 A115181
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 14 2006
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