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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
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
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-François Alcover, Jul 03 2018, after Andrew Howroyd *)
CROSSREFS
Column k=5 of A305059.
Sequence in context: A101973 A244968 A071258 * A000368 A232765 A094255
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