A121190 Number of non-overlapping unbranched staggered conformers of alkanes with 2n-1 nodes and symmetry point group C_s.

0, 0, 1, 3, 9, 26, 73, 200, 561, 1568

Offset: 1

Author

N. J. A. Sloane, Aug 17 2006

Keywords

• nonn
• more

Comments

In Cyvin et al. (Z. Naturforsch. 1995), the terms 0, 1, 3, 9, and 26 appear in Table 1 on p. 860 as odd terms under the group C_s (corresponding to C_3 H_8, C_5 H_12, C_7 H_16, C_9 H_20, and C_11 H_24, respectively). - Petros Hadjicostas, Jul 24 2019

Further comments from Petros Hadjicostas, Jul 24 2019, added by N. J. A. Sloane, Jul 24 2019: (Start)

While studying this sequence, I looked at A121179 and its references. The sequence b(n) (with g.f. b(x)) that appears in some of the papers below is actually sequence A001764 for which there is an enormous literature.

I have a strong suspicion that the current sequence A121190 is related to these two sequences a(n) = A121179(n) and b(n) = A001764 (or to their relatives c(n), d(n), and e(n) that appear in Wang et al. (1996)). (End)

Links

• J. Brunvoll, B. N. Cyvin, E. Brendsdal, and S. J. Cyvin, Computerized enumeration of staggered alkane conformers, Computers Chem. 19 (1995), 379-388.
• S. J. Cyvin, Algebraic solution for the numbers of staggered conformers of alkanes, J. Math. Chem. 17 (1995), 291-293.
• S. J. Cyvin, J. Brunvoll, B. N. Cyvin, and W. Lüttke, Enumeration of the staggered conformers of alkanes, Zeitschrift für Naturforschung A 50(9) (1995), 857-863.
• S. J. Cyvin, B. N. Cyvin, J. Brunvoll, and Jianji Wang, Enumeration of staggered conformers of alkanes and monocyclic cycloalkanes, J. Molec. Struct. 445 (1998), 127-137. See Table 3, column C_s, rows labeled "unbranched", for the terms a(6)-a(10).
• S. J. Cyvin, Jianji Wang, J. Brunvoll, Shiming Cao, Ying Li, B. N. Cyvin, and Yugang Wang, Staggered conformers of alkanes: complete solution of the enumeration problem, J. Molec. Struct. 413-414 (1997), 227-239.
• Jianji Wang, Shiming Cao, and Ying Li, An algebraic solution for the numbers of staggered conformers of alkanes, J. Math. Chem. 20 (1996), 211-212.

Crossrefs

Cf. A001764, A121179.

Extensions

Name clarified by Hakan Icoz, Aug 27 2021