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A036671
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Number of isomers C_n H_{2n} without double bonds.
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10
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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
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OFFSET
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1,4
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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FORMULA
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Polya reference gives an explicit g.f.; so does Parks et al.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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