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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
OFFSET
4,3
LINKS
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
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