login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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