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 A308745 Expansion of 1/(1 - x*(1 + x)/(1 - x^2*(1 + x^2)/(1 - x^3*(1 + x^3)/(1 - x^4*(1 + x^4)/(1 - ...))))), a continued fraction. 0
 1, 1, 2, 4, 8, 17, 36, 76, 161, 342, 726, 1542, 3276, 6960, 14788, 31422, 66767, 141872, 301464, 640584, 1361188, 2892417, 6146164, 13060136, 27751818, 58970564, 125308114, 266270558, 565805452, 1202295228, 2554789536, 5428741218, 11535678790, 24512475453 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..33. FORMULA From Vaclav Kotesovec, Jun 25 2019: (Start) a(n) ~ c * d^n, where d = 2.124927028900893046638236231387101475346473032396641627320401... c = 0.386397654364351443933577245182777062935616240164642598839093... (End) From Peter Bala, Dec 18 2020 Conjectural g.f.: 1/(2 - (1 + x)/(1 - x^2/(2 - (1 + x^3)/(1 - x^4/(2 - (1 + x^5)/(1 - x^6/(2 - ... ))))))). More generally it appears that 1/(1 - t*x*(1 + u*x)/(1 - t*x^2*(1 + u*x^2)/(1 - t*x^3*(1 + u*x^3)/(1 - t*x^4*(1 + u*x^4)/(1 - ... ))))) = 1/(1 + u - (u + t*x)/(1 - t*x^2/(1 + u - (u + t*x^3)/(1 - t*x^4/(1 + u - (u + t*x^5)/(1 - ... )))))). (End) MATHEMATICA nmax = 33; CoefficientList[Series[1/(1 + ContinuedFractionK[-x^k (1 + x^k), 1, {k, 1, nmax}]), {x, 0, nmax}], x] CROSSREFS Cf. A005169, A053254, A092848, A143064. Sequence in context: A292322 A008999 A052903 * A226729 A063457 A262735 Adjacent sequences: A308742 A308743 A308744 * A308746 A308747 A308748 KEYWORD nonn,easy AUTHOR Ilya Gutkovskiy, Jun 21 2019 STATUS approved

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Last modified October 4 00:24 EDT 2023. Contains 365872 sequences. (Running on oeis4.)