A261767 - OEIS

%I #18 Oct 31 2015 15:36:07

%S 1,1,1,1,3,3,1,7,18,8,1,15,99,64,30,1,31,510,560,300,144,1,63,2745,

%T 4800,3150,1728,840

%N Triangle read by rows: T(n,k) is the number of subpermutations of an n-set, whose orbits are each of size at most k with at least one orbit of size exactly k.

%D A. Laradji and A. Umar, On the number of subpermutations with fixed orbit size, Ars Combinatoria, 109 (2013), 447-460.

%F T(n, k) = A261763(n, k) - A261763(n, k-1), T(n, n) = A261766(n) for all n not equal to 1 and T(1, 1) = 1.

%e T(3, 2) = 18 because there are 18 subpermutations on {1,2,3} whose orbits are each of size at most 2 with at least one orbit of size exactly 2, namely: (1 2 --> 2 1), (1 3 --> 3 1), (2 3 --> 3 2), (123 --> 213), (123 --> 321), (123 --> 132); (1-->2), (1-->3), (2-->1), (2-->3), (3-->1), (3-->2); (13-->23), (12-->32), (23-->13), (32-->33), (23-->21), (13-->12).

%e Triangle starts:

%e 1;

%e 1, 1;

%e 1, 3, 3;

%e 1, 7, 18, 8;

%e 1, 15, 99, 64, 30;

%e 1, 31, 510, 560, 300, 144;

%e ...

%Y Cf. A261762, A261763, A261764, A261765, A261766, A261767.

%Y Row sums give A002720.

%K nonn,tabl,more

%O 0,5

%A _Samira Stitou_, Sep 21 2015