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Search: id:A099783
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| A099783 |
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Sum C(n-k,2k)3^(n-2k), k=0..floor(n/3). |
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+0
1
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| 1, 3, 9, 30, 108, 405, 1548, 5967, 23085, 89451, 346842, 1345248, 5218263, 20242872, 78528609, 304640595, 1181814705, 4584708702, 17785841652, 68998115709, 267670245492, 1038395956527, 4028337876861, 15627474388899, 60624993311226
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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In general a(n)=sum{k=0..floor(n/3), C(n-k,2k)u^k*v^(n-3k)} has g.f. (1-v*x)/((1-v*x)^2-u*x^2) and satisfies the recurrence a(n)=2uv*a(n-1)-v^2*a(n-2)+u*a(n-3).
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FORMULA
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G.f.: (1-3x)/((1-3x)^2-3x^3); a(n)=6a(n-1)-9a(n-2)+3a(n-3).
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CROSSREFS
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Adjacent sequences: A099780 A099781 A099782 this_sequence A099784 A099785 A099786
Sequence in context: A036727 A053022 A128725 this_sequence A032125 A091699 A129167
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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), Oct 26 2004
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