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A120333 Number of monocyclic skeletons with n carbon atoms and a ring size of 5. 3
1, 1, 4, 9, 28, 71, 198, 521, 1418, 3773, 10153, 27114, 72705, 194531, 521447, 1397482, 3749836, 10067417, 27057233, 72779710, 195963184, 528127752, 1424707167, 3846943003, 10397057771, 28125235102, 76149287981, 206351312858, 559642013499, 1519019192097 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,3

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).

LINKS

Andrew Howroyd, Table of n, a(n) for n = 5..200

EXAMPLE

If n=10 then the number of monocyclic skeletons with ring size of five is 71.

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 + 5, 5];

Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Jul 03 2018, after Andrew Howroyd *)

CROSSREFS

Column k=5 of A305059.

Sequence in context: A101973 A244968 A071258 * A000368 A232765 A094255

Adjacent sequences:  A120330 A120331 A120332 * A120334 A120335 A120336

KEYWORD

nonn

AUTHOR

Parthasarathy Nambi, Aug 13 2006

EXTENSIONS

More terms from N. J. A. Sloane, Aug 27 2006

Terms a(26) and beyond from Andrew Howroyd, May 24 2018

STATUS

approved

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Last modified July 17 02:50 EDT 2019. Contains 325092 sequences. (Running on oeis4.)