A333083 Number of permutations sigma of [n] such that all values k * sigma(k) for 1 <= k <= n are pairwise distinct.
1, 1, 1, 3, 13, 67, 305, 2359, 16495, 141643, 1273691, 15580299, 152788607, 2206382433, 28916044241, 399450183613
Offset: 0
Examples
In the n=3 case:
| sigma(1),sigma(2),sigma(3)
----+---------------------------
1 | [1, 2, 3]
2 | [2, 3, 1]
3 | [3, 1, 2]
Links
- Wikipedia, Permutation
Crossrefs
Cf. A333082.
Programs
-
Mathematica
Table[ Count[ Length@ Union[# Range@ n] & /@ Permutations@ Range@ n, n], {n, 0, 9}] (* Giovanni Resta, Mar 09 2020 *) -
PARI
a(n) = {my(nb=0); forperm([1..n], p, if (#Set(vector(n, k, k*p[k])) == n, nb++);); nb;} \\ Michel Marcus, Mar 09 2020 -
Ruby
def A(n) (1..n).to_a.permutation.select{|i| (1..n).map{|j| i[j - 1] * j}.uniq.size == n}.size end def A333083(n) (0..n).map{|i| A(i)} end p A333083(9)
Extensions
a(13)-a(15) from Giovanni Resta, Mar 09 2020