A005957 Number of acyclic ketone and aldehyde stereo-isomers with n carbon atoms.

1, 1, 2, 3, 8, 18, 47, 123, 338, 935, 2657, 7616, 22138, 64886, 191873, 571169, 1711189, 5153883, 15599094, 47415931, 144692886, 443091572, 1361233280, 4194107380, 12957209782, 40128629400, 124562327944, 387467513732, 1207633413980

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

It seems that, starting with a(2), this is row j = 1 in Table 3 (p. 176) in Wang et al. (2003). This is also corroborated by the title of the table: "The numbers f_{ij} of stereo isomers of acyclic saturated compounds consisting of C, O, and H, C_i H_{2i+2} O_j". Such a claim, if true, can probably be proved by using Eqs. (5), (6), and (7) on pp. 175-176 of the paper. - Petros Hadjicostas, Jul 24 2019

References

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

Links

• R. C. Read, The Enumeration of Acyclic Chemical Compounds, pp. 25-61 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976. [Annotated scanned copy] See p. 44.
• Jianji Wang, Ruxiong Li, and Shen Wang, Enumeration of isomers of acyclic saturated hydroxyl ethers, Journal of Mathematical Chemistry 33 (2003), 171-179.

Formula

G.f.: (1/2)*x*(B^2(x)+B(x^2)) where B(x) is the g.f. for A000625. - Sean A. Irvine, Nov 12 2016

Extensions

a(23) corrected, title improved, and more terms from Sean A. Irvine, Nov 12 2016