%I
%S 1,1,3,6,53,496,81096,35292601,211275732504203,5013078952131335869356,
%T 4188494841905497365271738826910705731652978,
%U 13998172580873019733546655911268420464183123192214609601699428961
%N Number of structural alkanes with combinatorial diameter n.
%D R. Davies and P. J. Freyd, C_{167}H_{336} is The Smallest Alkane with More Realizable Isomers than the Observable Universe has Particles, Journal of Chemical Education, Vol. 66, April 1989, pp. 278281.
%e There are 53 such alkanes where the longest chain of carbon atoms is of length 5.
%t rid[0]=1; rid[r_] := rid[r]=1+Binomial[rid[r1]+2, 3]; rd[r_] := rid[r]rid[r1]; td[1]=1; td[r_] := If[EvenQ[r], Binomial[rd[r/2]+1, 2], Binomial[rid[(r1)/2]+3, 4]rd[(r1)/2]Binomial[rid[(r3)/2]+2, 3]Binomial[rid[(r3)/2]+3, 4]]; td/@Range[12]
%Y Cf. A000602, A000628, A067609, A067610.
%K nonn
%O 1,3
%A Peter Freyd (pjf(AT)saul.cis.upenn.edu), Feb 02 2002
%E Edited by _Dean Hickerson_, Feb 11 2002
