cp's OEIS Frontend

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

%I A000633 M2667 N1065 #27 May 21 2023 22:22:42
%S A000633 1,1,3,7,18,42,109,269,691,1759,4542,11733,30559,79743,209136,549959,
%T A000633 1451178,3838925,10182703,27069940,72121696,192527888,514908269,
%U A000633 1379454526,3701556642,9947456861,26770280299,72138803942,194638086892,525773470041,1421850523472
%N A000633 Number of acyclic quaternary ammonium ions with n carbon atoms.
%C A000633 First page of Henze paper gives a(15)=11733, a(20)=1451178.
%C A000633 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
%D A000633 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000633 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000633 H. R. Henze and C. M. Blair, <a href="http://dx.doi.org/10.1021/ja01316a050">The number of structural isomers of the more important types of aliphatic compounds</a>, J. Amer. Chem. Soc., 56 (1) (1934), 157-157.
%H A000633 H. R. Henze and C. M. Blair, <a href="/A000632/a000632.pdf">The number of structural isomers of the more important types of aliphatic compounds</a>, J. Amer. Chem. Soc., 56 (1) (1934), 157-157. (Annotated scanned copy)
%H A000633 David Consiglio, Jr., <a href="/A000633/a000633.png">Illustration of n=4, 5, and 6</a>
%H A000633 David Consiglio, Jr., <a href="/A000633/a000633_1.png">Illustration of n=7</a>
%H A000633 David Consiglio, Jr., <a href="/A000633/a000633_2.png">Illustration of n=8</a>
%F A000633 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
%Y A000633 Cf. A000598.
%K A000633 nonn
%O A000633 4,3
%A A000633 _N. J. A. Sloane_
%E A000633 Revised by _David Consiglio, Jr._ and _Sean A. Irvine_, May 21 2023