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%I M2288 N0905
%S 0,0,1,0,1,1,3,3,9,15,38,73,174,380,915,2124,5134,12281,30010,73401,
%T 181835,452165,1133252,2851710,7215262,18326528,46750268,119687146,
%U 307528889,792716193,2049703887,5314775856,13817638615,36012395538
%N Number of bicentered hydrocarbons with n atoms.
%D Busacker and Saaty, Finite Graphs and Networks, 1965, p. 201 (they reproduce Cayley's mistakes).
%D A. Cayley, "On the mathematical theory of isomers", Phil. Mag. vol. 67 (1874), 444-447.
%D A. Cayley, "Ueber die analytischen Figuren, welche in der Mathematik Baeume genannt werden...", 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="/A000200/b000200.txt">Table of n, a(n) for n = 0..60</a>
%H H. Bottomley, <a href="/A000602/a000602.gif">Illustration of initial terms of A000022, A000200, A000602</a>
%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 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%H N. J. A. Sloane, <a href="/A000602/a000602.txt">Maple program and first 60 terms for A000022, A000200, A000598, A000602, A000678</a>
%p 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 # Maple code continues from A000022: bicentered == unordered pair of ternary trees of the same height:
%Y Cf. A000220, A000602, A010373.
%K nonn,nice
%O 0,7
%A _N. J. A. Sloane_, E. M. Rains (rains(AT)caltech.edu)
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