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Search: id:A000200
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| A000200 |
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Number of bicentered hydrocarbons with n atoms.
(Formerly M2288 N0905)
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+0
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; listen)
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OFFSET
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0,7
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
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LINKS
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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
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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
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Cf. A000220, A000602, A010373.
Sequence in context: A147471 A166265 A062510 this_sequence A100744 A089892 A038221
Adjacent sequences: A000197 A000198 A000199 this_sequence A000201 A000202 A000203
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), E. M. Rains (rains(AT)caltech.edu)
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