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 A005309 M1125 #33 Apr 13 2022 13:25:17
%S A005309 1,0,2,4,8,16,32,60,114,212,384,692,1232,2160,3760,6480,11056,18728,
%T A005309 31474,52492,86976,143176,234224,380988,616288,991624,1587600,2529560,
%U A005309 4011808,6334656,9960080,15596532,24327122,37801568,58525152,90291232,138825416
%N A005309 Fermionic string states.
%C A005309 See the reference for precise definition.
%C A005309 The g.f. -(1-2*z+2*z**2)/(-1+2*z) conjectured by _Simon Plouffe_ in his 1992 dissertation is not correct.
%D A005309 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005309 Vaclav Kotesovec, <a href="/A005309/b005309.txt">Table of n, a(n) for n = 0..1000</a>
%H A005309 T. Curtright, <a href="http://inspirehep.net/record/234762/files/CountingStringStates.pdf">Counting symmetry patterns in the spectra of strings</a>, in H. J. de Vega and N. Sánchez, editors, String Theory, Quantum Cosmology and Quantum Gravity. Integrable and Conformal Invariant Theories. World Scientific, Singapore, 1987, pp. 304-333, eq. (3.39) and Table 3.
%H A005309 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A005309 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%F A005309 G.f. Product_{k>=1} ((1+x^k)/(1-x^k))^(k-1). - _Vaclav Kotesovec_, Aug 19 2015
%F A005309 Convolution of A052847 and A052812. - _Vaclav Kotesovec_, Aug 19 2015
%F A005309 a(n) ~ 2^(7/18) * (7*Zeta(3))^(1/36) * exp(1/12 - Pi^4/(336*Zeta(3)) - Pi^2 * n^(1/3) / (2^(5/3)*(7*Zeta(3))^(1/3)) + 3/2 * (7*Zeta(3)/2)^(1/3) * n^(2/3)) / (A * sqrt(3) * n^(19/36)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant. - _Vaclav Kotesovec_, Aug 19 2015
%Y A005309 Cf. A156616, A261451, A261386, A261452, A261389.
%K A005309 nonn
%O A005309 0,3
%A A005309 _N. J. A. Sloane_