cp's OEIS Frontend

A000623 Number of monosubstituted alkanes C(n)H(2n+1)-X of the form shown in the Comments lines that are stereoisomers.

%I A000623 M4125 N1712 #21 Feb 01 2022 01:05:40
%S A000623 0,0,0,0,0,0,6,18,66,208,646,1962,5962,18014,54578,165650,504220,
%T A000623 1539330,4713742,14475936,44578668,137634872,425970290,1321323952,
%U A000623 4107268140,12792332438,39915708564,124762612530,390593588402,1224681912368,3845387953884,12090382743374
%N A000623 Number of monosubstituted alkanes C(n)H(2n+1)-X of the form shown in the Comments lines that are stereoisomers.
%C A000623 ....X
%C A000623 ....|
%C A000623 R-C-R' (tertiary)
%C A000623 ....|
%C A000623 ....R"
%C A000623 Let the entries in the nine columns of Blair and Henze's Table I (JACS 54 (1932), p. 1098) be denoted by Ps(n), Pn(n), Ss(n), Sn(n), Ts(n), Tn(n), As(n), An(n), T(n) respectively (here P = Primary, S = Secondary, T = Tertiary, s = stereoisomers, n = non-stereoisomers and the last column T(n) gives total).
%C A000623 Then Ps (and As) = A000620, Pn (and An, Sn) = A000621, Ss = A000622, Ts = this sequence, Tn = A000624, T = A000625. Recurrences generating these sequences are given in the Maple program in A000620.
%D A000623 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000623 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000623 Vaclav Kotesovec, <a href="/A000623/b000623.txt">Table of n, a(n) for n = 1..1930</a>
%H A000623 C. M. Blair and H. R. Henze, <a href="http://dx.doi.org/10.1021/ja01342a036">The number of stereoisomeric and non-stereoisomeric mono-substitution products of the paraffins</a>, J. Amer. Chem. Soc., 54 (3) (1932), 1098-1106.
%H A000623 C. M. Blair and H. R. Henze, <a href="/A000620/a000620.pdf">The number of stereoisomeric and non-stereoisomeric mono-substitution products of the paraffins</a>, J. Amer. Chem. Soc., 54 (3) (1932), 1098-1105. (Annotated scanned copy)
%F A000623 a(n) ~ c * b^n / n^(3/2), where b = 3.287112055584474991259... (see A239803), c = 0.069641252627300354415... (see A239808). - _Vaclav Kotesovec_, Mar 27 2014
%Y A000623 Cf. A000620-A000625, A239803, A239808.
%K A000623 nonn
%O A000623 1,7
%A A000623 _N. J. A. Sloane_
%E A000623 Additional comments from Bruce Corrigan, Nov 04 2002