|
| |
|
|
A029852
|
|
Number of connected functions on n points with a loop of length 3.
|
|
2
|
|
|
|
1, 1, 3, 9, 23, 62, 169, 451, 1217, 3291, 8916, 24243, 66155, 181053, 497134, 1369064, 3780942, 10469573, 29063361, 80867990, 225508124, 630145449, 1764240907, 4948365051, 13902893423, 39124094362, 110265280739, 311208414556, 879523722747, 2488832434859
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
3,3
|
|
|
LINKS
|
Alois P. Heinz, Table of n, a(n) for n = 3..1000
|
|
|
FORMULA
|
G.f.: A(x) = ( B(x)^3 + 2*B(x^3) )/3 where B(x) is o.g.f. for A000081. - Geoffrey Critzer, Aug 09 2013
|
|
|
MATHEMATICA
|
nn = 20; f[x_] := Sum[a[n] x^n, {n, 0, nn}]; sol =
SolveAlways[
0 == Series[
f[x] - x Product[1/(1 - x^i)^a[i], {i, 1, nn}], {x, 0, nn}],
x]; b = Flatten[Table[a[n], {n, 1, nn}] /. sol]; CoefficientList[
Series[CycleIndex[CyclicGroup[3], s] /.
Table[s[i] -> Sum[b[[k]] x^(k*i), {k, 1, nn}], {i, 1, 3}], {x, 0,
nn}], x] (* Geoffrey Critzer, Aug 08 2013 *)
|
|
|
CROSSREFS
|
Cf. A000081.
Sequence in context: A061647 A207008 A077996 * A282732 A047085 A253244
Adjacent sequences: A029849 A029850 A029851 * A029853 A029854 A029855
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Christian G. Bower
|
|
|
STATUS
|
approved
|
| |
|
|
