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Search: id:A008998
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| A008998 |
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a(n) = 2 a(n-1) + a(n-3). |
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+0
5
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| 1, 2, 4, 9, 20, 44, 97, 214, 472, 1041, 2296, 5064, 11169, 24634, 54332, 119833, 264300, 582932, 1285697, 2835694, 6254320, 13794337, 30424368, 67103056, 148000449, 326425266, 719953588, 1587907625
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A transform of A000079 under the mapping mapping g(x)->(1/(1-x^3))g(x/(1-x^3)). - Paul Barry (pbarry(AT)wit.ie), Oct 20 2004
The binomial transform yields 1,3,9,..., i.e. A049220 without the leading zeros. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 15 2008
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 452
B. Rittaud, On the Average Growth of Random Fibonacci Sequences, Journal of Integer Sequences, 10 (2007), Article 07.2.4.
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FORMULA
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a(n)=sum{k=0..floor(n/3), binomial(n-2k, k)2^(n-3k)} - Paul Barry (pbarry(AT)wit.ie), Oct 20 2004
O.g.f.: 1/(1-2x-x^3). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 15 2008
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MAPLE
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A008998 := proc(n) option remember; if n <= 2 then 2^n else 2*A008998(n-1)+A008998(n-3); fi; end;
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CROSSREFS
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Sequence in context: A130587 A129988 A035530 this_sequence A141016 A024736 A024562
Adjacent sequences: A008995 A008996 A008997 this_sequence A008999 A009000 A009001
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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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