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A088209 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], ... 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Denominators form the Les Marvin sequence: A007502(n+1).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

FORMULA

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

EXAMPLE

a(3)/A007502(4) = [1;1,1,4] = 14/9.

MATHEMATICA

f[n_] := Numerator@  FromContinuedFraction@ Join[ Table[1, {n}], {n + 1}]; Array[f, 30, 0] (* Robert G. Wilson v, Mar 04 2012 *)

PROG

(Haskell)

a088209 n = a088209_list !! n

a088209_list = zipWith (+) a000045_list $ tail a045925_list

-- Reinhard Zumkeller, Oct 01 2012, Mar 04 2012

CROSSREFS

Cf. A007502 (the denominators).

a(n) = A109754(n, n+2) = A101220(n, 0, n+2).

Cf. A000045.

Cf. A045925.

Sequence in context: A018084 A285447 A140741 * A089074 A125176 A153234

Adjacent sequences:  A088206 A088207 A088208 * A088210 A088211 A088212

KEYWORD

frac,nonn

AUTHOR

Paul D. Hanna, Sep 23 2003

STATUS

approved

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Last modified February 19 14:22 EST 2018. Contains 299333 sequences. (Running on oeis4.)