This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A308745 #16 Aug 17 2025 01:52:04
%S A308745 1,1,2,4,8,17,36,76,161,342,726,1542,3276,6960,14788,31422,66767,
%T A308745 141872,301464,640584,1361188,2892417,6146164,13060136,27751818,
%U A308745 58970564,125308114,266270558,565805452,1202295228,2554789536,5428741218,11535678790,24512475453
%N 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.
%F A308745 From _Vaclav Kotesovec_, Jun 25 2019: (Start)
%F A308745 a(n) ~ c * d^n, where
%F A308745 d = 2.124927028900893046638236231387101475346473032396641627320401...
%F A308745 c = 0.386397654364351443933577245182777062935616240164642598839093... (End)
%F A308745 From _Peter Bala_, Dec 18 2020: (Start)
%F A308745 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 - ... ))))))).
%F A308745 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)
%t A308745 nmax = 33; CoefficientList[Series[1/(1 + ContinuedFractionK[-x^k (1 + x^k), 1, {k, 1, nmax}]), {x, 0, nmax}], x]
%Y A308745 Cf. A005169, A053254, A092848, A143064.
%K A308745 nonn,easy
%O A308745 0,3
%A A308745 _Ilya Gutkovskiy_, Jun 21 2019