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A088209
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Numerators of convergents of the continued fraction with the n+1 partial quotients: [1;1,1,...(n 1's)...,1,n+1], starting with [1], [1;2], [1;1,3], [1;1,1,4], ...
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5
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1, 3, 7, 14, 28, 53, 99, 181, 327, 584, 1034, 1817, 3173, 5511, 9527, 16402, 28136, 48109, 82023, 139481, 236631, 400588, 676822, 1141489, 1921993, 3231243, 5424679, 9095126, 15230452, 25475429, 42566379, 71052157, 118489383
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OFFSET
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0,2
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COMMENTS
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Denominators form the Les Marvin sequence: A007502(n+1).
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 0..1000
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FORMULA
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G.f.: (1-x-x^3)/(1-x-x^2)^2.
a(n)=Fib(n)+(n+1)Fib(n+1). - Paul Barry, Apr 20 2004
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EXAMPLE
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a(3)/A007502(4) = [1;1,1,4] = 14/9.
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MATHEMATICA
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f[n_] := Numerator@ FromContinuedFraction@ Join[ Table[1, {n}], {n + 1}]; Array[f, 30, 0] (* Robert G. Wilson v, Mar 4 2012 *)
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PROG
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(Haskell)
a088209 n = a088209_list !! n
a088209_list = zipWith (+) a000045_list $ tail a045925_list
-- Reinhard Zumkeller, Oct 01 2012, Mar 04 2012
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CROSSREFS
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Cf. A007502 (the denominators).
a(n) = A109754(n, n+2) = A101220(n, 0, n+2).
Cf. A000045.
Cf. A045925.
Sequence in context: A029879 A018084 A140741 * A089074 A125176 A153234
Adjacent sequences: A088206 A088207 A088208 * A088210 A088211 A088212
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KEYWORD
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frac,nonn
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AUTHOR
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Paul D. Hanna, Sep 23 2003
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STATUS
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approved
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