%I A067608
%S A067608 1,1,3,6,53,496,81096,35292601,211275732504203,5013078952131335869356,
%T A067608 4188494841905497365271738826910705731652978,
%U A067608 13998172580873019733546655911268420464183123192214609601699428961
%N A067608 Number of structural alkanes with combinatorial diameter n.
%D A067608 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. 278-281.
%e A067608 There are 53 such alkanes where the longest chain of carbon atoms is 
               of length 5.
%t A067608 rid[0]=1; rid[r_] := rid[r]=1+Binomial[rid[r-1]+2, 3]; rd[r_] := rid[r]-rid[r-1]; 
               td[1]=1; td[r_] := If[EvenQ[r], Binomial[rd[r/2]+1, 2], Binomial[rid[(r-1)/
               2]+3, 4]-rd[(r-1)/2]Binomial[rid[(r-3)/2]+2, 3]-Binomial[rid[(r-3)/
               2]+3, 4]]; td/@Range[12]
%Y A067608 Cf. A000602, A000628, A067609, A067610.
%Y A067608 Sequence in context: A056447 A056437 A012275 this_sequence A023177 A132474 
               A032070
%Y A067608 Adjacent sequences: A067605 A067606 A067607 this_sequence A067609 A067610 
               A067611
%K A067608 nonn
%O A067608 1,3
%A A067608 Peter Freyd (pjf(AT)saul.cis.upenn.edu), Feb 02 2002
%E A067608 Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Feb 11 2002