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A000022 Number of centered hydrocarbons with n atoms.
(Formerly M0358 N0135)

%I M0358 N0135

%S 0,1,0,1,1,2,2,6,9,20,37,86,181,422,943,2223,5225,12613,30513,74883,

%T 184484,458561,1145406,2879870,7274983,18471060,47089144,120528657,

%U 309576725,797790928,2062142876,5345531935,13893615154,36201693122

%N Number of centered hydrocarbons with n atoms.

%D R. G. Busacker and T. L. Saaty, Finite Graphs and Networks, McGraw-Hill, NY, 1965, p. 201. (They reproduce Cayley's mistakes.)

%D A. Cayley, "Über die analytischen Figuren, welche in der Mathematik Bäume genannt werden und ihre Anwendung auf die Theorie chemischer Verbindungen", Chem. Ber. 8 (1875), 1056-1059.

%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 N. J. A. Sloane, <a href="/A000022/b000022.txt">Table of n, a(n) for n = 0..60</a>

%H Jean-François Alcover, <a href="/A000602/a000602_1.txt">Mathematica program translated from N. J. A. Sloane's Maple program for A000022, A000200, A000598, A000602, A000678</a>

%H H. Bottomley, <a href="/A000602/a000602.gif">Illustration of initial terms of A000022, A000200, A000602</a>

%H A. Cayley, <a href="http://www.archive.org/stream/collectedmathema09cayl#page/202">On the mathematical theory of isomers</a>, Phil. Mag. vol. 67 (1874), 444-447.

%H H. R. Henze, C. M. Blair, <a href="http://dx.doi.org/10.1021/ja01359a027">The number of structurally isomeric alcohols of the methanol series</a>, J. Amer. Chem. Soc., 53 (8) (1931), 3042-3046.

%H H. R. Henze, C. M. Blair, <a href="http://dx.doi.org/10.1021/ja01359a034">The number of isomeric hydrocarbons of the methane series</a>, J. Amer. Chem. Soc., 53 (8) (1931), 3077-3085.

%H E. M. Rains and N. J. A. Sloane, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">On Cayley's Enumeration of Alkanes (or 4-Valent Trees)</a>, J. Integer Sequences, Vol. 2 (1999), Article 99.1.1.

%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/sg.txt">My favorite integer sequences</a>, in Sequences and their Applications (Proceedings of SETA '98).

%H N. J. A. Sloane, <a href="/A000602/a000602.txt">Maple program and first 60 terms for A000022, A000200, A000598, A000602, A000678</a>

%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%p # We continue from the Maple code in A000678: Unordered 4-tuples of ternary trees with one of height i and others of height at most i-1:

%p N := 45: i := 1: while i<(N+1) do Tb := t[ i ]-t[ i-1 ]: Ts := t[ i ]-1: Q2 := series(Tb*Ts+O(z^(N+1)),z,200): q2[ i ] := Q2: i := i+1; od: q2[ 0 ] := 0: q[ -1 ] := 0:

%p for i from 0 to N do c[ i ] := series(q[ i ]-q[ i-1 ]-q2[ i ]+O(z^(N+1)),z,200); od:

%p # erase height information: i := 'i': cent := series(sum(c[ i ],i=0..N),z,200); G000022 := cent; A000022 := n->coeff(G000022,z,n);

%p # continued in A000200.

%Y A000022 + A000200 = A000602. Cf. A010372.

%K nonn,easy,nice

%O 0,6

%A _N. J. A. Sloane_, E. M. Rains (rains(AT)caltech.edu)

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Last modified July 24 08:32 EDT 2017. Contains 289717 sequences.