|
| |
|
|
A333083
|
|
Number of permutations sigma of [n] such that all values k * sigma(k) for 1 <= k <= n are pairwise distinct.
|
|
2
|
|
|
|
1, 1, 1, 3, 13, 67, 305, 2359, 16495, 141643, 1273691, 15580299, 152788607, 2206382433, 28916044241, 399450183613
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,4
|
|
|
LINKS
|
Table of n, a(n) for n=0..15.
Wikipedia, Permutation
|
|
|
EXAMPLE
|
In the n=3 case:
| sigma(1),sigma(2),sigma(3)
----+---------------------------
1 | [1, 2, 3]
2 | [2, 3, 1]
3 | [3, 1, 2]
|
|
|
MATHEMATICA
|
Table[ Count[ Length@ Union[# Range@ n] & /@ Permutations@ Range@ n, n], {n, 0, 9}] (* Giovanni Resta, Mar 09 2020 *)
|
|
|
PROG
|
(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)
(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
|
|
|
CROSSREFS
|
Cf. A333082.
Sequence in context: A142979 A302303 A201713 * A298611 A136784 A284717
Adjacent sequences: A333080 A333081 A333082 * A333084 A333085 A333086
|
|
|
KEYWORD
|
nonn,more
|
|
|
AUTHOR
|
Seiichi Manyama, Mar 07 2020
|
|
|
EXTENSIONS
|
a(13)-a(15) from Giovanni Resta, Mar 09 2020
|
|
|
STATUS
|
approved
|
| |
|
|
