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Search: id:A006478
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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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+0
7
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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
(list; graph; listen)
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OFFSET
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3,2
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REFERENCES
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S. 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.
K. J. Overholt, Efficiency of the Fibonacci search method, Nordisk Tidskr. Informationsbehandling (BIT) 13 (1973), 92-96.
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LINKS
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S. 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.
S. 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 (benoit7848c(AT)orange.fr), Jan 26 2003
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MAPLE
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A006478:=-1/(z-1)/(z**2+z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Cf. A006479. Partial sums of A001629(n).
Adjacent sequences: A006475 A006476 A006477 this_sequence A006479 A006480 A006481
Sequence in context: A078409 A036642 A000235 this_sequence A104187 A131051 A051633
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KEYWORD
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nonn
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AUTHOR
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njas
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