A067608 Number of structural alkanes with combinatorial diameter n.

1, 1, 3, 6, 53, 496, 81096, 35292601, 211275732504203, 5013078952131335869356, 4188494841905497365271738826910705731652978, 13998172580873019733546655911268420464183123192214609601699428961

Offset: 1

Author

Peter Freyd (pjf(AT)saul.cis.upenn.edu), Feb 02 2002

Keywords

• nonn

Examples

			There are 53 such alkanes where the longest chain of carbon atoms is of length 5.
		

References

• 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.

Crossrefs

Cf. A000602, A000628, A067609, A067610.

Programs

Mathematica

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]

Extensions

Edited by Dean Hickerson, Feb 11 2002