A000622 Number of monosubstituted alkanes C(n)H(2n+1)-X of the form shown in the Comments lines that are stereoisomers.

0, 0, 0, 2, 4, 14, 34, 98, 270, 768, 2192, 6360, 18576, 54780, 162658, 486154, 1461174, 4413988, 13393816, 40807290, 124783604, 382842018, 1178140170, 3635626680, 11247841040, 34880346840, 108402132234, 337576497920, 1053229357732, 3291813720292, 10305275270364

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

R-CH-X (secondary)

.....|

.....R'

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).

Then Ps (and As) = A000620, Pn (and An, Sn) = A000621, Ss = this sequence, Ts = A000623, Tn = A000624, T = A000625. Recurrences generating these sequences are given in the Maple program in A000620.

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

• Vaclav Kotesovec, Table of n, a(n) for n = 1..1930
• C. M. Blair and H. R. Henze, The number of stereoisomeric and non-stereoisomeric mono-substitution products of the paraffins, J. Amer. Chem. Soc., 54 (3) (1932), 1098-1106.
• C. M. Blair and H. R. Henze, The number of stereoisomeric and non-stereoisomeric mono-substitution products of the paraffins, J. Amer. Chem. Soc., 54 (3) (1932), 1098-1105. (Annotated scanned copy)

Crossrefs

Cf. A000620-A000625, A239803, A239807.

Formula

a(n) ~ c * b^n / n^(3/2), where b = 3.287112055584474991259... (see A239803), c = 0.171310881484463744523... (see A239807). - Vaclav Kotesovec, Mar 27 2014

Extensions

Additional comments from Bruce Corrigan, Nov 04 2002