
REFERENCES

A. T. Balaban, J. W. Kennedy and L. V. Quintas, The number of alkanes having n carbons and a longest chain of length d, J. Chem. Education, 65 (No. 4, 1988), 304313.
N. L. Biggs et al., Graph Theory 17361936, Oxford, 1976, p. 62 (quoting Cayley, who is wrong).
A. Cayley, On the mathematical theory of isomers, Phil. Mag. vol. 67 (1874), 444447 (a(6) is wrong).
J. L. Faulon, D. Visco and D. Roe, Enumerating Molecules, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, WileyVCH, 2005.
R. A. Fisher, Contributions to Mathematical Statistics, Wiley, 1950, 41.397.
J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 529.
Handbook of Combinatorics, NorthHolland '95, p. 1963.
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Knop, Mueller, Szymanski and Trinajstich, Computer generation of certain classes of molecules.
Camden A. Parks and James B. Hendrickson, Enumeration of monocyclic and bicyclic carbon skeletons, J. Chem. Inf. Comput. Sci., vol. 31, 334339 (1991).
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MAPLE

N := 45; G000598 := 0: i := 0: while i<(N+1) do G000598 := series(1+z*(G000598^3/6+subs(z=z^2, G000598)*G000598/2+subs(z=z^3, G000598)/3)+O(z^(N+1)), z, N+1): t[ i ] := G000598: i := i+1: od: A000598 := n>coeff(G000598, z, n);
[Another Maple program for g.f. G000598] G000598 := 1; f := proc(n) global G000598; coeff(series(1+(1/6)*x*(G000598^3+3*G000598*subs(x=x^2, G000598)+2*subs(x=x^3, G000598)), x, n+1), x, n); end; for n from 1 to 50 do G000598 := series(G000598+f(n)*x^n, x, n+1); od; G000598;
spec := [S, {Z=Atom, S=Union(Z, Prod(Z, Set(S, card=3)))}, unlabeled]: [seq(combstruct[count](spec, size=n), n=0..20)];
