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Search: id:A115178
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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
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OFFSET
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0,5
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COMMENT
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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
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a(n)=sum{k=0..floor(n/2), C(k)C(k,n-2k)}.
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CROSSREFS
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Cf. A007477.
Sequence in context: A002956 A027167 A136336 this_sequence A049885 A129682 A129981
Adjacent sequences: A115175 A115176 A115177 this_sequence A115179 A115180 A115181
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 14 2006
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