%I #41 Nov 19 2019 03:27:42

%S 1,1,1,2,3,2,7,7,9,17,9,31,31,41,72,41,120,120

%N Isomer numbers for the fluorenoid/fluoranthenoid constant-isomer series.

%C This allows a single pentagonal ring among otherwise hexagonal rings.

%C The terms occur in groups of 5: X, X, Y, Z, Y, ..., except for the 0th term (corresponding to the C5H5 series). [Edited by _Petros Hadjicostas_, Nov 17 2019]

%C From _Petros Hadjicostas_, Nov 17 2019: (Start)

%C From all the papers listed in the Links, the author of this sequence considers Dias (1991) as the basic one for this sequence.

%C The starting compounds for each constant-isomer series are as follows (with the number of isomers inside parentheses): C5H5 (1), C9H7 (1), C12H8 (1), C15H9 (2), C18H10 (3), C23H11 (2), C26H12 (7), C31H13 (7), C36H14 (9), C41H15 (17), C48H16 (9), C53H17 (31), C60H18 (31), C67H19 (41), C74H20 (72), C83H21 (41), C90H22 (120), C99H23 (120), C108H24 (...), C117H25 (...), C128H26 (...), where "..." means that the corresponding number of isomers is not listed in the papers (probably because they are not known yet).

%C Starting with each one of the above compounds, the corresponding constant-isomer series is generated by the operator P(C_n H_s) -> C_{n + 2*s + 5} H_{s + 5} successively. For example, the first series is C5H5 -> C20H10 -> C45H15 -> C80H20 -> ...

%C The starting compound of each constant-isomer series is C_n H_s, where n = s + 2 + 2*floor((1/10) * (s^2 - 7*s + 6)), for s = 5, 7, 8, 9, 10, 11, 12, ... (i.e., we skip s = 6). Thus, a(0) = 1 corresponds to s = 5 (i.e., C5H5), and for m >= 1, a(m) corresponds to s = m + 6, i.e., to C_n H_s, where n = s + 2 + 2*floor((1/10) * (s^2 - 7*s + 6)). See Cyvin et al. (1993, p. 233). (End)

%D J. R. Dias, The Periodic Table Set as a Unifying Concept in Going from Benzenoid Hydrocarbons to Fullerene Carbons, in "The Periodic Table: Into the 21st Century", Edited by D.H. Rouvray and R. B. King, Research Studies Press Ltd, Baldock, Hertfordshire, England, 2004, 371-396. [See Section 5.2.]

%H J. Brunvoll, B. N. Cyvin, S. J. Cyvin, G. Brinkmann, and J. Bornhoft, <a href="http://zfn.mpdl.mpg.de/data/Reihe_A/51/ZNA-1996-51a-1073.pdf">Enumeration of chemical isomers of polyclic conjugated hydrocarbons with six-membered and five-membered rings</a>, Z. Naturforsch. 51a (1996), pp. 1073-1078.

%H S. J. Cyvin, B. N. Cyvin and J. Brunvoll, <a href="https://doi.org/10.1016/0166-1280(93)87079-S">Graph-theoretical studies on fluoranthenoids and fluorenoids</a>, J. Molec. Struct. (Theochem) 281(2-3) (1993), pp. 229-236.

%H Jerry Ray Dias, <a href="https://doi.org/10.1016/0009-2614(91)80131-G">Series of fluorenoiod/fluroranthenoid hydrocarbons having a constant number of isomers</a>, Chem. Phys. Lett. 185 (1-2) (1991), pp. 10-15. [See Table 2, p. 13.] (*)

%H Jerry Ray Dias, <a href="https://doi.org/10.1021/ci00011a017">Deciphering the information content of chemical formulas: Chemical and structural characteristics and enumeration of indacenes</a>, J. Chem. Inf. Comput. Sci. 32 (1992), pp. 203-209. [Table III, p. 206, gives the number of isomers for indacenoid hydrocarbon constant-isomer series that appear in A129023. The paper, however, contains a useful explanation of the whole theory.]

%H Jerry Ray Dias, <a href="https://doi.org/10.1021/ci00011a017">Notes on constant-isomer series</a>, J. Chem. Inf. Comput. Sci. 33 (1993), pp. 117-127.

%H Jerry Ray Dias, <a href="https://doi.org/10.1016/0166-218X(95)00012-G">Graph theoretical invariants and elementary subgraphs of polyhex and polypent/polyhex systems of chemical relevance</a>, Discr. App. Math. 67 (1-3) (1996), pp. 79-114. [This paper contains a clear mathematical definition of all the symbols used in the chemical papers. It is also contains a description of the so-called "aufbau principle".]

%H Jerry Ray Dias, <a href="https://doi.org/10.1007/s10910-010-9671-9">Structure/formula informatics of isomeric sets of fluoranthemoid/fluorenoid and indacenoid hydrocarbons</a>, Journal of Mathematical Chemistry 48(2) (2010), pp. 313-329. [It contains more recent information about this sequence and other similar sequences, A129012-A129021 and A129023.]

%Y Cf. A129012-A129021, A129023.

%K nonn,more

%O 0,4

%A _N. J. A. Sloane_, May 10 2007