A063832 Number of structurally isomeric homologs with molecular formula C_{3+n} H_{6+2n}.

1, 1, 3, 6, 15, 33, 83, 196, 491, 1214, 3068, 7754, 19834, 50872, 131423, 340763, 887839, 2321193, 6090979, 16031341, 42319223, 112003765, 297164610, 790190726, 2105607907, 5621642203, 15036126167, 40284850520, 108102408101

Offset: 0

Author

Vladeta Jovovic, Aug 21 2001

Keywords

• nonn
• nice

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).
• G. Polya and R. C. Read, Combinatorial Enumeration of Groups, Graphs and Chemical Compounds, Springer-Verlag, 1987, p. 63.
• Ching-Wan Lam, "Enumeration of isomers of alkylcyclopropanes by means of alkyl 1,1-biradicals", J. Math. Chem., 27 (2000), 23-25. [From Parthasarathy Nambi, Aug 24 2008]

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• G. Polya, Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen, Acta Math. 68 (1937), 145-254.

Crossrefs

Column k=3 of A305059.

Column 3 of a table (in Parks and Hendrickson) in which the subsequent columns are A116719, A120333, A120779, A120790, A120795, A121156, A121157.

Programs

Mathematica

G[n_] := Module[{g}, Do[g[x_] = 1 + x*(g[x]^3/6 + g[x^2]*g[x]/2 + g[x^3]/3) + O[x]^n // Normal, {n}]; g[x]];
T[n_, k_] := Module[{t = G[n], g}, t = x*((t^2 + (t /. x -> x^2))/2); g[e_] = (Normal[t + O[x]^Quotient[n, e]] /. x -> x^e) + O[x]^n // Normal; Coefficient[(Sum[EulerPhi[d]*g[d]^(k/d), {d, Divisors[k]}]/k + If[OddQ[ k], g[1]*g[2]^Quotient[k, 2], (g[1]^2 + g[2])*g[2]^(k/2-1)/2])/2, x, n]];
a[n_] := T[n + 3, 3];
Table[a[n], {n, 0, 29}] (* Jean-François Alcover, Jul 03 2018, after Andrew Howroyd *)

Formula

G.f.: A(x) = cycle_index(S3[S2]B(x)), where B(x) is g.f. for A000598.