|
Search: id:A121352
|
|
|
| A121352 |
|
Number of different, not necessarily connected, unlabeled trivalent diagrams of size n. |
|
+0
9
|
|
| 1, 1, 2, 4, 7, 10, 24, 37, 63, 112, 200, 318, 607, 1058, 1814, 3247, 6004, 10316, 19048, 35478, 63496, 117023, 223822, 408121, 766661, 1484363, 2775201, 5270079, 10357605, 19714259, 37970066, 75439670, 146103241, 284719527, 571706625
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Equivalently, the number of isomorphism class of PSL_2(ZZ) actions on finite sets of size n.
Also the number of (r,s) pair of permutions up to simultaneous conjugation, in S_n for which r is involutive i.e. r^2 = id and s is of weak order three i.e. s^3 = id.
|
|
LINKS
|
S. A. Vidal, Sur la Classification et le Denombrement des Sous-groupes du Groupe Modulaire et de leurs Classes de Conjugaison (in French), 2006, http://arXiv.org/abs/math.CO/0702223
|
|
MAPLE
|
mu := k -> `if`( k mod 2 = 0, 2/k, 1/k ) : nu := k -> `if`( k mod 3 = 0, 3/k, 1/k ) : u := (k, n) -> add(mu(k)^(n-2*k2)/(n-2*k2)!/k2!/(2*k)^k2, k2=0..floor(n/ 2)) : v := (k, n) -> add(nu(k)^(n-3*k3)/(n-3*k3)!/k3!/(3*k)^k3, k3=0..floor(n/ 3)) : N := 100 : ZF := 1 : for k from N to 1 by -1 do ZF := rem(ZF * add(n!*k^n*u(k, n)*v(k, n)*t^(k*n), n = 0..floor(N/ k)), t^(N+1), t) ; end do : sort(ZF, t, ascending);
|
|
CROSSREFS
|
Unconnected version of A121350.
Unlabeled version of A121357.
Cf. also A005133, A121355, A121356.
Sequence in context: A138827 A036685 A034744 this_sequence A134126 A091263 A101430
Adjacent sequences: A121349 A121350 A121351 this_sequence A121353 A121354 A121355
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Samuel Alexandre Vidal (samuel.vidal(AT)free.fr), Jul 23 2006
|
|
|
Search completed in 0.002 seconds
|
