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A022087
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Fibonacci sequence beginning 0 4.
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7
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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, 14098312, 22811548, 36909860, 59721408, 96631268
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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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Table of n, a(n) for n=0..37.
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to linear recurrences with constant coefficients, signature (1,1).
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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, May 20 2006
G.f.: 4x/(1-x-x^2). [From Philippe DELEHAM, Nov 19 2008]
a(n)=F(n+9)-17F(n+3), n>=0, F(n)=A000045. [From Manuel Valdivia, 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, 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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PROG
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(PARI) a(n)=4*fibonacci(n) \\ Charles R Greathouse IV, Jun 05, 2011
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CROSSREFS
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Sequence in context: A194697 A194696 A002368 * A095294 A190100 A030168
Adjacent sequences: A022084 A022085 A022086 * A022088 A022089 A022090
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KEYWORD
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nonn,easy,changed
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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