A005960 Number of acyclic disubstituted alkanes with n carbon atoms and distinct substituents. (Formerly M2747)

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

1,2

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

Table of n, a(n) for n=1..27.

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.

Formula

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

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 *)

Crossrefs

Cf. A193418.

Sequence in context: A002712 A192679 A193418 * A273716 A184120 A215512

Adjacent sequences: A005957 A005958 A005959 * A005961 A005962 A005963

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved