OFFSET
4,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 4..200
Camden A. Parks and James B. Hendrickson, Enumeration of monocyclic and bicyclic carbon skeletons, J. Chem. Inf. Comput. Sci., vol. 31, 334-339 (1991).
EXAMPLE
If n=5 then the number of monocyclic skeletons with ring size of four is 1.
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, 4];
Table[a[n], {n, 4, 30}] (* Jean-François Alcover, Jul 03 2018, after Andrew Howroyd *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Parthasarathy Nambi, Aug 13 2006
EXTENSIONS
More terms from N. J. A. Sloane, Aug 27 2006
a(5) corrected and terms a(26) and beyond from Andrew Howroyd, May 24 2018
STATUS
approved