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A000200
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Number of bicentered hydrocarbons with n atoms.
(Formerly M2288 N0905)
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9
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0, 0, 1, 0, 1, 1, 3, 3, 9, 15, 38, 73, 174, 380, 915, 2124, 5134, 12281, 30010, 73401, 181835, 452165, 1133252, 2851710, 7215262, 18326528, 46750268, 119687146, 307528889, 792716193, 2049703887, 5314775856, 13817638615, 36012395538
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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REFERENCES
| Busacker and Saaty, Finite Graphs and Networks, 1965, p. 201 (they reproduce Cayley's mistakes).
A. Cayley, "On the mathematical theory of isomers", Phil. Mag. vol. 67 (1874), 444-447.
A. Cayley, "Ueber die analytischen Figuren, welche in der Mathematik Baeume genannt werden...", Chem. Ber. 8 (1875), 1056-1059.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| N. J. A. Sloane, Table of n, a(n) for n = 0..60
H. Bottomley, Illustration of initial terms of A000022, A000200, A000602
E. M. Rains and N. J. A. Sloane, On Cayley's Enumeration of Alkanes (or 4-Valent Trees)., J. Integer Sequences, Vol. 2 (1999), Article 99.1.1.
Index entries for sequences related to trees
N. J. A. Sloane, Maple program and first 60 terms for A000022, A000200, A000598, A000602, A000678
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MAPLE
| 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);
# Maple code continues from A000022: bicentered == unordered pair of ternary trees of the same height:
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CROSSREFS
| Cf. A000220, A000602, A010373.
Sequence in context: A105423 A147471 A062510 * A100744 A089892 A038221
Adjacent sequences: A000197 A000198 A000199 * A000201 A000202 A000203
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), E. M. Rains (rains(AT)caltech.edu)
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