login
Number of acyclic ethylene derivatives with n carbon atoms.
(Formerly M3286)
0

%I M3286 #15 Dec 26 2016 15:22:49

%S 1,1,4,6,18,42,118,314,895,2521,7307,21238,62566,185310,553288,

%T 1660490,5011299,15190665,46244031,141296042,433204573,1332261200,

%U 4108833222,12704949506,39379343929,122327632914,380778749899,1187544117426

%N Number of acyclic ethylene derivatives with n carbon atoms.

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

%H R. C. Read, <a href="/A000598/a000598.pdf">The Enumeration of Acyclic Chemical Compounds</a>, pp. 25-61 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976. [Annotated scanned copy] See p. 44.

%F 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

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

%K nonn

%O 2,3

%A _N. J. A. Sloane_.

%E More terms from _Sean A. Irvine_, Nov 12 2016