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Number of paraffins C_n H_{2n} X_2 with n carbon atoms.
(Formerly M1185 N0457)
1

%I M1185 N0457 #28 Jan 29 2022 00:59:56

%S 1,2,4,9,21,52,129,332,859,2261,5983,15976,42836,115469,312246,847241,

%T 2304522,6283327,17164401,46972357,128741107,353345434,970999198,

%U 2671347292,7356752678,20279171785,55948407837,154479213626,426845422807,1180229767202

%N Number of paraffins C_n H_{2n} X_2 with n carbon atoms.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H H. R. Henze and C. M. Blair, <a href="http://dx.doi.org/10.1021/ja01316a050">The number of structural isomers of the more important types of aliphatic compounds</a>, J. Amer. Chem. Soc., 56 (1) (1934), 157-157.

%H H. R. Henze and C. M. Blair, <a href="/A000632/a000632.pdf">The number of structural isomers of the more important types of aliphatic compounds</a>, J. Amer. Chem. Soc., 56 (1) (1934), 157-157. (Annotated scanned copy)

%H G. Polya, <a href="http://dx.doi.org/10.1524/zkri.1936.93.1.415">Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen</a>, Zeit. f. Kristall., 93 (1936), 415-443; line 4 of Table I.

%H G. Polya, <a href="/A000598/a000598_3.pdf">Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen</a>, Zeit. f. Kristall., 93 (1936), 415-443; Table I, line 2. (Annotated scanned copy)

%H R. C. Read, <a href="/A000598/a000598.pdf">The Enumeration of Acyclic Chemical Compounds</a>, pp. 25-61 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976. [Annotated scanned copy] See p. 28.

%F G.f.: (1/2) * (1/(1-x*R(x)) + (1+x*R(x)) / (1-x^2*R(x^2))) where R(x) is the g.f. for A000642 [From Polya paper]. - _Sean A. Irvine_, Oct 04 2016

%K nonn,easy,nice

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Oct 04 2016