%I A000022 M0358 N0135
%S A000022 0,1,0,1,1,2,2,6,9,20,37,86,181,422,943,2223,5225,12613,30513,74883,
%T A000022 184484,458561,1145406,2879870,7274983,18471060,47089144,120528657,
%U A000022 309576725,797790928,2062142876,5345531935,13893615154,36201693122
%N A000022 Number of centered hydrocarbons with n atoms.
%D A000022 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000022 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000022 R. G. Busacker and T. L. Saaty, Finite Graphs and Networks,mcGraw-Hill, 
               NY, 1965, p. 201 (they reproduce Cayley's mistakes).
%D A000022 A. Cayley, "On the mathematical theory of isomers", Phil. Mag. vol. 67 
               (1874), 444-447.
%D A000022 A. Cayley, "Ueber die analytischen Figuren, welche in der Mathematik 
               Baeume genannt werden...", Chem. Ber. 8 (1875), 1056-1059.
%D A000022 H. R. Henze and C. M. Blair, The number of structurally isomeric alcohols 
               of the methanol series, J. Amer. Chem. Soc., 53 (1931), 3042-3046.
%D A000022 H. R. Henze and C. M. Blair, The number of isomeric hydrocarbons of the 
               methane series, J. Amer Chem Soc. 53 (1931) 3077-3085.
%H A000022 N. J. A. Sloane, <a href="b000022.txt">Table of n, a(n) for n = 0..60</
               a>
%H A000022 H. Bottomley, <a href="a602.gif">Illustration of initial terms of A000022, 
               A000200, A000602</a>
%H A000022 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 A000022 N. J. A. Sloane, <a href="http://www.research.att.com/~njas/doc/sg.txt">
               My favorite integer sequences</a>, in Sequences and their Applications 
               (Proceedings of SETA '98).
%H A000022 N. J. A. Sloane, <a href="a000602.txt">Maple program and first 60 terms 
               for A000022, A000200, A000598, A000602, A000678</a>
%H A000022 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%p A000022 # 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 A000022 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 A000022 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 A000022 # erase height information: i := 'i': cent := series(sum(c[ i ],i=0..N),
               z,200); G000022 := cent; A000022 := n->coeff(G000022,z,n);
%p A000022 # continued in A000200.
%Y A000022 A000022+A000200=A000602. Cf. A010372.
%Y A000022 Sequence in context: A094485 A021819 A000021 this_sequence A034805 A051765 
               A077063
%Y A000022 Adjacent sequences: A000019 A000020 A000021 this_sequence A000023 A000024 
               A000025
%K A000022 nonn,easy,nice
%O A000022 0,6
%A A000022 N. J. A. Sloane (njas(AT)research.att.com), E. M. Rains (rains(AT)caltech.edu)