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
Keywords
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
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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
Comments