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Search: id:A022087
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| A022087 |
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Fibonacci sequence beginning 0 4. |
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+0
6
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| 0, 4, 4, 8, 12, 20, 32, 52, 84, 136, 220, 356, 576, 932, 1508, 2440, 3948, 6388, 10336, 16724, 27060, 43784, 70844, 114628, 185472, 300100, 485572, 785672, 1271244, 2056916, 3328160, 5385076, 8713236
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 18.
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LINKS
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Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n) = round( (8phi-4)/5 phi^n) (works for n>2) - Thomas Baruchel, Sep 08 2004
a(n) = 4F(n) = F(n-2) + F(n) + F(n+2), with F(n) = A000045(n).
a(n) = A119457(n+2,n-1) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 20 2006
G.f.: 4x/(1-x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 19 2008]
a(n)=F(n+9)-17F(n+3), n>=0, F(n)=A000045. [From Manuel Valdivia (mvaldivia(AT)ugr.es), Dec 15 2009]
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MAPLE
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a := n-> (Matrix([[4, 0]]). Matrix([[1, 1], [1, 0]])^n)[1, 2]: seq (a(n), n=0..32); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 17 2008]
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MATHEMATICA
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a={}; b=0; c=4; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 9, 1}]; a (Vladimir Orlovsky, Jul 22 2008)
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CROSSREFS
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Sequence in context: A086663 A003829 A002368 this_sequence A095294 A030168 A112435
Adjacent sequences: A022084 A022085 A022086 this_sequence A022088 A022089 A022090
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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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