A000623 Number of monosubstituted alkanes C(n)H(2n+1)-X of the form shown in the Comments lines that are stereoisomers. (Formerly M4125 N1712)

0, 0, 0, 0, 0, 0, 6, 18, 66, 208, 646, 1962, 5962, 18014, 54578, 165650, 504220, 1539330, 4713742, 14475936, 44578668, 137634872, 425970290, 1321323952, 4107268140, 12792332438, 39915708564, 124762612530, 390593588402, 1224681912368, 3845387953884, 12090382743374

Offset

1,7

Comments

....X

....|

R-C-R' (tertiary)

....|

....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 = A000622, Ts = this sequence, 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)

Formula

a(n) ~ c * b^n / n^(3/2), where b = 3.287112055584474991259... (see A239803), c = 0.069641252627300354415... (see A239808). - Vaclav Kotesovec, Mar 27 2014

Crossrefs

Cf. A000620-A000625, A239803, A239808.

Sequence in context: A074427 A034751 A200151 * A304941 A129369 A095853

Adjacent sequences: A000620 A000621 A000622 * A000624 A000625 A000626

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Additional comments from Bruce Corrigan, Nov 04 2002

Status

approved