A261336 Number of achiral molecules containing two linear or branched chiral alkyl chains of n carbon atoms each.

0, 0, 0, 1, 3, 10, 30, 88, 255, 742, 2157, 6312, 18563, 54932, 163479, 489264, 1471692, 4447896, 13500689, 41140608, 125818217, 386050543, 1188093392, 3666547089, 11344058829, 35180323336, 109339097119, 340508394528

Offset: 1

Author

Matthew S. MacLennan, Aug 15 2015

Keywords

• nonn

Comments

a(n) is half the number of chiral planted trees of n nodes (A005628(n)). This number is half the total number of chiral alkanes because the two alkyl chains are required to have the same length with opposite chirality at each chiral center: For each chiral alkane, there is only one other with opposite chirality at each center. The two alkyl chains are attached to a scaffold with a mirror plane between them, thus imparting achirality on the whole molecule. Although such a molecule contains chiral centers, the molecule itself is not chiral--its mirror image is superposable on itself. These compounds are called meso compounds in chemistry.

Links

• Matthew S. MacLennan, On the Number of Phthalates, Physically Chemist Blog, 17 July 2015.

Crossrefs

Equals half A005628.

Formula

a(n) = A005628(n) / 2.