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 A227045 G.f.: 1/(1 - q/G(0)) where G(k) = 1 - q^(k+1) / (1 - q^(k+1) / G(k+1) ). 1
 1, 1, 2, 5, 13, 35, 95, 260, 713, 1959, 5386, 14815, 40759, 112151, 308609, 849240, 2337009, 6431246, 17698332, 48704714, 134032593, 368850417, 1015056867, 2793383746, 7687248186, 21154913043, 58217239536, 160210872557, 440892153268, 1213312738702, 3338974845151, 9188688696438 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..1000 FORMULA G.f.: 1/(1-q/ (1-q/(1-q/ (1-q^2/(1-q^2/ (1-q^3/(1-q^3/ (1-q^4/(1-q^4/ (1-q^5/(1-q^5/ (1-...))))))))))) ). G.f. A(x) = 1/(1 - B(x)) where B(x) is the g.f. of A006958. a(n) ~ c * d^n, where d = 2.751949072495748078279227332764623096815571855905843246297955690122791154... and c = 0.215973947378529032758849789768859077066690378163074586384819930605436492... - Vaclav Kotesovec, Sep 05 2017 MATHEMATICA nmax = 40; CoefficientList[Series[1/(1 - x/Fold[(1 - #2/#1) &, 1, Reverse[x^(Range[nmax + 2] - Floor[Range[nmax + 2]/2])]]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 05 2017 *) PROG (PARI) N = 66;  q = 'q + O('q^N); G(k) = if(k>N, 1, 1 - q^(k+1) / (1 - q^(k+1) / G(k+1) ) ); gf = 1 /(1- q/G(0)); Vec(gf) CROSSREFS Cf. A006958 (g.f.: 1/G(0), where G(k) = 1 - q^(k+1) / (1 - q^(k+1)/G(k+1) ) ). Cf. A226729 (g.f.: 1/G(0), where G(k) = 1 - q^(k+1) / (1 - q^(k+1)/G(k+2) ) ). Cf. A226728 (g.f.: 1/G(0), where G(k) = 1 + q^(k+1) / (1 - q^(k+1)/G(k+2) ) ). Cf. A227309 (g.f.: 1/G(0), where G(k) = 1 - q^(k+1) / (1 - q^(k+2)/G(k+1) ) ). Cf. A227310 (g.f.: 1/G(0), where G(k) = 1 + (-q)^(k+1) / (1 - (-q)^(k+1)/G(k+1) ) ). Sequence in context: A054657 A024576 A057960 * A007075 A000107 A063028 Adjacent sequences:  A227042 A227043 A227044 * A227046 A227047 A227048 KEYWORD nonn AUTHOR Joerg Arndt, Jul 06 2013 STATUS approved

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Last modified October 21 09:37 EDT 2018. Contains 316411 sequences. (Running on oeis4.)