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A006478
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a(n)=a(n-1)+a(n-2)+F(n)-1, where F() = Fibonacci numbers A000045.
(Formerly M2733)
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9
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1, 3, 8, 18, 38, 76, 147, 277, 512, 932, 1676, 2984, 5269, 9239, 16104, 27926, 48210, 82900, 142055, 242665, 413376, 702408, 1190808, 2014608, 3401833, 5734251, 9650312
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OFFSET
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3,2
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COMMENTS
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Partial sums of A001629.
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REFERENCES
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K. J. Overholt, Efficiency of the Fibonacci search method, Nordisk Tidskr. Informationsbehandling (BIT) 13 (1973), 92-96.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=3..29.
Index to sequences with linear recurrences with constant coefficients, signature (3,-1,-3,1,1).
_Simon Plouffe_, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
_Simon Plouffe_, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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If offset 0: a(n)=1+((n-2)*F(n+2)+(3*n+1)*F(n+3))/5, g.f.: 1/((1-x)*(1-x-x^2)^2).
a(n)=sum(k=0, n-1, sum(i=0, k, F(i)*F(k-i))). - Benoit Cloitre, Jan 26 2003
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MAPLE
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A006478:=-1/(z-1)/(z**2+z-1)**2; [Simon Plouffe in his 1992 dissertation with offset 0.]
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MATHEMATICA
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f[x_] = -1 + 3 x - x^2 - 3 x^3 + x^4 + x^5
Table[SeriesCoefficient[
Series[-1/f[x], {x, 0, 30}], n], {n, 0, 30}]- Roger Bagula Dec 4 2010
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CROSSREFS
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Cf. A006479.
Sequence in context: A078409 A036642 A000235 * A104187 A051633 A131051
Adjacent sequences: A006475 A006476 A006477 * A006479 A006480 A006481
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KEYWORD
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nonn
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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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