A005960 Number of acyclic disubstituted alkanes with n carbon atoms and distinct substituents.

1, 3, 8, 23, 69, 208, 636, 1963, 6099, 19059, 59836, 188576, 596252, 1890548, 6008908, 19139155, 61074583, 195217253, 624913284, 2003090071, 6428430129, 20653101216, 66420162952, 213802390264, 688796847976, 2220789746752, 7165331870036

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Acyclic alkanes of the form C_nH_mXY with X != Y. For X = Y see A005961. - Sean A. Irvine, Nov 12 2016

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• R. C. Read, The Enumeration of Acyclic Chemical Compounds, pp. 25-61 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976. [Annotated scanned copy] See p. 44.

Crossrefs

Cf. A193418.

Programs

Mathematica

terms = 27; (* B = g.f. for A000625 *) B[] = 0; Do[B[x] = 1 + x*((B[x]^3 + 2*B[x^3])/3) + O[x]^(terms + 1) // Normal, terms + 1];
A[x_] = 1/(1 - x*B[x]^2) + O[x]^(terms + 1);
CoefficientList[A[x], x] // Rest (* Jean-François Alcover, Jan 10 2018 *)

Formula

G.f.: 1/(1-x*B(x)^2) where B(x) is the g.f. for A000625. - Sean A. Irvine, Nov 12 2016

Extensions

More terms and title improved by Sean A. Irvine, Nov 12 2016