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Number of paraffins C_n H_{2n} X Y with n carbon atoms.
(Formerly M1418 N0555)
1

%I M1418 N0555 #39 Dec 19 2021 09:40:21

%S 0,1,2,5,12,31,80,210,555,1479,3959,10652,28760,77910,211624,576221,

%T 1572210,4297733,11767328,32266801,88594626,243544919,670228623,

%U 1846283937,5090605118,14047668068,38794922293,107215238057,296501478704

%N Number of paraffins C_n H_{2n} X Y 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 T. D. Noe, <a href="/A000635/b000635.txt">Table of n, a(n) for n = 0..200</a>

%H Frederic Chyzak, <a href="http://algo.inria.fr/libraries/autocomb/Polya-html/Polya.html">Enumerating alcohols and other classes of chemical molecules</a>

%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; Table I line 3.

%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 3. (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.: A(x) = B(x)/(1-B(x)), B(x) = g.f. for A000642.

%t terms = 29; B[_] = 0; Do[B[x_] = 1 + (1/6)*x*(B[x]^3 + 3*B[x]*B[x^2] + 2*B[x^3]) + O[x]^terms // Normal, terms];

%t B642[x_] = (1/2)*x*(B[x^2] + B[x]^2) + O[x]^terms;

%t A[x_] = B642[x]/(1 - B642[x]);

%t CoefficientList[A[x], x] (* _Jean-François Alcover_, Oct 21 2011, updated Jan 10 2018 *)

%K nonn,easy,nice

%O 0,3

%A _N. J. A. Sloane_