%I A000200 M2288 N0905
%S A000200 0,0,1,0,1,1,3,3,9,15,38,73,174,380,915,2124,5134,12281,30010,73401,
%T A000200 181835,452165,1133252,2851710,7215262,18326528,46750268,119687146,
%U A000200 307528889,792716193,2049703887,5314775856,13817638615,36012395538
%N A000200 Number of bicentered hydrocarbons with n atoms.
%D A000200 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000200 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000200 Busacker and Saaty, Finite Graphs and Networks, 1965, p. 201 (they reproduce 
               Cayley's mistakes).
%D A000200 A. Cayley, "On the mathematical theory of isomers", Phil. Mag. vol. 67 
               (1874), 444-447.
%D A000200 A. Cayley, "Ueber die analytischen Figuren, welche in der Mathematik 
               Baeume genannt werden...", Chem. Ber. 8 (1875), 1056-1059.
%H A000200 N. J. A. Sloane, <a href="b000200.txt">Table of n, a(n) for n = 0..60</
               a>
%H A000200 H. Bottomley, <a href="a602.gif">Illustration of initial terms of A000022, 
               A000200, A000602</a>
%H A000200 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 A000200 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%H A000200 N. J. A. Sloane, <a href="a000602.txt">Maple program and first 60 terms 
               for A000022, A000200, A000598, A000602, A000678</a>
%p A000200 N := 45: for i from 1 to N do tt := t[ i ]-t[ i-1 ]; b[ i ] := series((tt^2+subs(z=z^2,
               tt))/2+O(z^(N+1)),z,200): od: i := 'i': bicent := series(sum(b[ i 
               ],i=1..N),z,200); G000200 := bicent; A000200 := n->coeff(G000200,
               z,n);
%p A000200 # Maple code continues from A000022: bicentered == unordered pair of 
               ternary trees of the same height:
%Y A000200 Cf. A000220, A000602, A010373.
%Y A000200 Sequence in context: A147471 A166265 A062510 this_sequence A100744 A089892 
               A038221
%Y A000200 Adjacent sequences: A000197 A000198 A000199 this_sequence A000201 A000202 
               A000203
%K A000200 nonn,easy,nice
%O A000200 0,7
%A A000200 N. J. A. Sloane (njas(AT)research.att.com), E. M. Rains (rains(AT)caltech.edu)