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A000022 Number of centered hydrocarbons with n atoms.
(Formerly M0358 N0135)
10
0, 1, 0, 1, 1, 2, 2, 6, 9, 20, 37, 86, 181, 422, 943, 2223, 5225, 12613, 30513, 74883, 184484, 458561, 1145406, 2879870, 7274983, 18471060, 47089144, 120528657, 309576725, 797790928, 2062142876, 5345531935, 13893615154, 36201693122 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

REFERENCES

R. G. Busacker and T. L. Saaty, Finite Graphs and Networks,mcGraw-Hill, NY, 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.

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.

H. R. Henze and C. M. Blair, The number of isomeric hydrocarbons of the methane series, J. Amer Chem Soc. 53 (1931) 3077-3085.

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).

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..60

Jean-Fran├žois Alcover, Mathematica program translated from N. J. A. Sloane's Maple program for A000022, A000200, A000598, A000602, A000678

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.

N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).

N. J. A. Sloane, Maple program and first 60 terms for A000022, A000200, A000598, A000602, A000678

Index entries for sequences related to trees

MAPLE

# 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:

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:

for i from 0 to N do c[ i ] := series(q[ i ]-q[ i-1 ]-q2[ i ]+O(z^(N+1)), z, 200); od:

# erase height information: i := 'i': cent := series(sum(c[ i ], i=0..N), z, 200); G000022 := cent; A000022 := n->coeff(G000022, z, n);

# continued in A000200.

CROSSREFS

A000022+A000200=A000602. Cf. A010372.

Sequence in context: A188808 A021819 A000021 * A034805 A192659 A051765

Adjacent sequences:  A000019 A000020 A000021 * A000023 A000024 A000025

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, E. M. Rains (rains(AT)caltech.edu)

STATUS

approved

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Last modified April 24 10:55 EDT 2014. Contains 240983 sequences.