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A036671
Number of isomers C_n H_{2n} without double bonds.
10
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
1,4
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.
FORMULA
Polya reference gives an explicit g.f.; so does Parks et al.
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
EXTENSIONS
More terms from Vladeta Jovovic, Aug 19 2001
STATUS
approved