I could not find these numbers in the two papers (Cyvin et al., 1997 and 1998). - Petros Hadjicostas, Jul 23 2019.
I agree that the terms 0, 0, 1, 3, 9, 26, 73, 200, 561, 1568 are not listed explicitly in either reference. However, they may result from one of the enumerations in the body of these papers (see for example the generating functions listed in Table 1 of the 1998 paper). For now, I added keyword "obsc". - N. J. A. Sloane, Jul 24 2019
In Cyvin et al. (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). We do not know, however, what comes after the number 26 (for C_13 H_28 and so on). It seems they got these numbers through computer programming, and they mention elsewhere in the paper that they may derive generating functions in future papers. - 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. I discovered that 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. Then given the definition of a(n) = A121179(n) (more precisely, given the definition of its g.f. in the various papers), it was easy to find the formula for a(n) = A121179(n).
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)
Table of n, a(n) for n=4..13.
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. Brumvoll, and Jianji Wang, Enumeration of staggered conformers of alkanes and monocyclic cycloalkanes, J. Molec. Struct. 445 (1998), 127-137.
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.