A000633 Number of acyclic quaternary ammonium ions with n carbon atoms. (Formerly M2667 N1065)

1, 1, 3, 7, 18, 42, 109, 269, 691, 1759, 4542, 11733, 30559, 79743, 209136, 549959, 1451178, 3838925, 10182703, 27069940, 72121696, 192527888, 514908269, 1379454526, 3701556642, 9947456861, 26770280299, 72138803942, 194638086892, 525773470041, 1421850523472

Offset

4,3

Comments

First page of Henze paper gives a(15)=11733, a(20)=1451178.

Equivalent to the number of rooted trees where the root (the nitrogen atom) has four children and each child is a nonempty unlabeled ternary tree. - Sean A. Irvine, May 21 2023

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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=4..34.

H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157.

H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157. (Annotated scanned copy)

David Consiglio, Jr., Illustration of n=4, 5, and 6

David Consiglio, Jr., Illustration of n=7

David Consiglio, Jr., Illustration of n=8

Formula

G.f. A(x) = cycle_index(S4, B(x)-1), where B(x) is g.f. for A000598 and S4 is the symmetric group on 4 elements. - Sean A. Irvine, May 21 2023

Crossrefs

Cf. A000598.

Sequence in context: A317546 A319001 A036669 * A340409 A091621 A129921

Adjacent sequences: A000630 A000631 A000632 * A000634 A000635 A000636

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Revised by David Consiglio, Jr. and Sean A. Irvine, May 21 2023

Status

approved