A005959 Number of acyclic ethylene derivatives with n carbon atoms. (Formerly M3286)

1, 1, 4, 6, 18, 42, 118, 314, 895, 2521, 7307, 21238, 62566, 185310, 553288, 1660490, 5011299, 15190665, 46244031, 141296042, 433204573, 1332261200, 4108833222, 12704949506, 39379343929, 122327632914, 380778749899, 1187544117426

Offset

2,3

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=2..29.

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.: (1/4)*x^2*(B(x)^4+3*B(x^2)^2) where B(x) is the g.f. for A000625. - Sean A. Irvine, Nov 12 2016

Example

G.f. = x^2 + x^3 + 4*x^4 + 6*x^5 + 18*x^6 + 42*x^7 + 118*x^8 + 314*X^9 + ...

Crossrefs

Sequence in context: A235344 A060667 A218065 * A057393 A196570 A274992

Adjacent sequences: A005956 A005957 A005958 * A005960 A005961 A005962

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from Sean A. Irvine, Nov 12 2016

Status

approved