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A005957 Number of acyclic ketone and aldehyde stereo-isomers with n carbon atoms.
(Formerly M0880)
1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

Table of n, a(n) for n=1..29.

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

CROSSREFS

Sequence in context: A241906 A079224 A002369 * A185171 A158448 A073192

Adjacent sequences:  A005954 A005955 A005956 * A005958 A005959 A005960

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

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

STATUS

approved

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Last modified November 16 17:04 EST 2019. Contains 329201 sequences. (Running on oeis4.)