A036671 Number of isomers C_n H_{2n} without double bonds.

0, 0, 1, 2, 5, 12, 29, 73, 185, 475, 1231, 3232, 8506, 22565, 60077, 160629, 430724, 1158502, 3122949, 8437289, 22836877, 61918923, 168139339, 457225555, 1244935251, 3393754661, 9261681937, 25301337669, 69184724389, 189349490641

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

References

• 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.
• 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.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500
• Michael A. Kappler, GENSMI: Exhaustive Enumeration of Simple Graphs.
• G. Polya, Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen, Acta Math. 68 (1937), 145-254.

Crossrefs

Cf. A000598, A000642, A001429.

Programs

PARI

\\ here G is A000598 as series
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}
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

Formula

Polya reference gives an explicit g.f.; so does Parks et al.

Extensions

More terms from Vladeta Jovovic, Aug 19 2001