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%I #25 Jan 10 2020 05:31:01
%S 0,0,1,2,5,12,29,73,185,475,1231,3232,8506,22565,60077,160629,430724,
%T 1158502,3122949,8437289,22836877,61918923,168139339,457225555,
%U 1244935251,3393754661,9261681937,25301337669,69184724389,189349490641
%N Number of isomers C_n H_{2n} without double bonds.
%C Equivalently, the number of simple unicyclic graphs on n unlabeled vertices with all degrees at most 4. See table 1 in Michael A. Kappler reference. - _Jonathan Vos Post_, Dec 07 2005, _Andrew Howroyd_, May 22 2018
%D Camden A. Parks and James B. Hendrickson, Enumeration of monocyclic and bicyclic carbon skeletons, J. Chem. Inf. Comput. Sci., vol. 31, 334-339 (1991). See page 335 Table 1.
%D J. B. Hendrikson and C. A. Parks, "Generation and Enumeration of Carbon skeletons", J. Chem. Inf. Comput. Sci, vol. 31 (1991) pp. 101-107. See Table 2, column 3 on page 103.
%H Andrew Howroyd, <a href="/A036671/b036671.txt">Table of n, a(n) for n = 1..500</a>
%H Michael A. Kappler, <a href="http://www.daylight.com/meetings/emug04/Kappler/GenSmi.html">GENSMI: Exhaustive Enumeration of Simple Graphs</a>.
%H G. Polya, <a href="https://projecteuclid.org/euclid.acta/1485888172">Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen</a>, Acta Math. 68 (1937), 145-254.
%F Polya reference gives an explicit g.f.; so does Parks et al.
%o (PARI) \\ here G is A000598 as series
%o G(n)={my(g=O(x)); for(n=1, n, g = 1 + x*(g^3/6 + subst(g,x,x^2)*g/2 + subst(g,x,x^3)/3) + O(x^n)); g}
%o seq(n)={my(t=G(n-2)); t=x*(t^2+subst(t,x,x^2))/2; my(g(e)=subst(t + O(x*x^(n\e)), x, x^e) + O(x*x^n)); Vec(sum(k=3, n, sumdiv(k, d, eulerphi(d)*g(d)^(k/d))/k + if(k%2, g(1)*g(2)^(k\2), (g(1)^2+g(2))*g(2)^(k/2-1)/2))/2, -n)} \\ _Andrew Howroyd_, May 22 2018
%Y Cf. A000598, A000642, A001429.
%K nonn,easy
%O 1,4
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, Aug 19 2001
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