|
|
A000200
|
|
Number of bicentered hydrocarbons with n atoms.
(Formerly M2288 N0905)
|
|
9
|
|
|
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;
text;
internal format)
|
|
|
OFFSET
|
0,7
|
|
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, "Über 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).
|
|
LINKS
|
|
|
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:
|
|
MATHEMATICA
|
n = 40; (* algorithm from Rains and Sloane *)
S3[f_, h_, x_] := f[h, x]^3/6 + f[h, x] f[h, x^2]/2 + f[h, x^3]/3;
T[-1, z_] := 1; T[h_, z_] := T[h, z] = Table[z^k, {k, 0, n}].Take[CoefficientList[z^(n+1) + 1 + S3[T, h-1, z]z, z], n+1];
Sum[Take[CoefficientList[z^(n+1) + (T[h, z] - T[h-1, z])^2/2 + (T[h, z^2] - T[h-1, z^2])/2, z], n+1], {h, 0, n/2}] (* Robert A. Russell, Sep 15 2018 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|