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Number of trisubstituted alkanes C_n H_{2n-1} X_2 Y with n carbon atoms.
1

%I #4 Mar 30 2012 16:50:47

%S 0,1,3,9,29,91,282,864,2624,7905,23665,70458,208813,616400,1813354,

%T 5318673,15559072,45410239,132258752,384493609,1115907585,3233782193,

%U 9358293913,27048189854,78087437216,225198736949,648826102943,1867669679538,5371673739750

%N Number of trisubstituted alkanes C_n H_{2n-1} X_2 Y with n carbon atoms.

%H N. J. A. Sloane, <a href="/A135142/b135142.txt">Table of n, a(n) for n = 0..100</a>

%H Frederic Chyzak, <a href="http://algo.inria.fr/libraries/autocomb/Polya-html/Polya.html">Enumerating alcohols and other classes of chemical molecules</a>

%p The following Maple commands are taken from the Chyzak web site:

%p with(combstruct);

%p gramm_Alkyl:=Alkyl=Prod(Carbon,Set(Alkyl,card<=3)),Carbon=Atom:

%p specs_Alkyl:=[Alkyl,{gramm_Alkyl},unlabeled]:

%p gramm_S1_Alkyl:=S1_Alkyl[X]=Union(Prod(Carbon,S1_Alkyl[X],Set(Alkyl,card<=2)),Prod(Prod(Carbon,X),Set(Alkyl,card<=2))),X=Epsilon:

%p specs_S1_Alkyl:=[S1_Alkyl[X],{gramm_S1_Alkyl,gramm_Alkyl},unlabeled]:

%p gramm_S2b_Alkyl:=S2_Alkyl[X,X]=Union(Prod(Carbon,S2_Alkyl[X,X],Set(Alkyl,card<=2)),Prod(Carbon,Union(Prod(S1_Alkyl[X],S1_Alkyl[X]),Prod(S1_Alkyl[X],X),Prod(X,X)),Set(Alkyl,card<=1))):

%p specs_S2b_Alkyl:=[S2_Alkyl[X,X],{gramm_S2b_Alkyl,gramm_S1_Alkyl,gramm_Alkyl},unlabeled]:

%p [seq(count(specs_S2b_Alkyl,size=i),i=0..50)];

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Feb 14 2008