A116719 Number of monocyclic skeletons with n carbon atoms and a ring size of 4.

1, 1, 4, 8, 24, 55, 147, 365, 954, 2431, 6327, 16369, 42743, 111595, 292849, 769805, 2030456, 5366844, 14222475, 37768154, 100510364, 267987501, 715847932, 1915406263, 5133382014, 13778469949, 37035674682, 99683747508, 268647638770, 724879674667, 1958151665752

Offset: 4

Author

Parthasarathy Nambi, Aug 13 2006

Keywords

• nonn

Examples

			If n=5 then the number of monocyclic skeletons with ring size of four is 1.
		

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).

Crossrefs

Column k=4 of A305059.

Cf. A063832.

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, 4];
Table[a[n], {n, 4, 30}] (* Jean-François Alcover, Jul 03 2018, after Andrew Howroyd *)

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