A000633 Number of acyclic quaternary ammonium ions with n carbon atoms.

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

Author

N. J. A. Sloane

Keywords

• nonn

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

• 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

Crossrefs

Cf. A000598.

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

Extensions

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