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 A116719 Number of monocyclic skeletons with n carbon atoms and a ring size of 4. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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 Column k=4 of A305059. Cf. A063832. Sequence in context: A115641 A153334 A332871 * A159612 A099176 A190156 Adjacent sequences:  A116716 A116717 A116718 * A116720 A116721 A116722 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

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Last modified May 25 07:56 EDT 2020. Contains 334585 sequences. (Running on oeis4.)