|
%I #16 Oct 07 2019 09:15:04
%S 1,2,4,12,40,132,428,1668,7628,36924,199000,1161824,7231332
%N Number of permutations of {1,2,...,n} such that for every k >= 1, the k-th differences are distinct.
%C a(n) <= A131529(n).
%e For n = 5 the a(5) = 40 solutions are one of following ten permutations, or a reversal, complement, or reversal and complement of one of these permutations:
%e [1,3,4,2,5]
%e [1,4,3,5,2]
%e [1,4,5,3,2]
%e [1,5,2,4,3]
%e [1,5,3,2,4]
%e [2,1,4,5,3]
%e [2,1,5,3,4]
%e [2,3,5,1,4]
%e [2,4,1,5,3]
%e [2,5,4,1,3]
%e As a non-example, [1,5,4,2,3] does not satisfy the k-th differences property, because while its first differences ([4,-1,-2,1]) and its second differences ([-5,-1,3]) are distinct, its third differences ([4,4]) are not.
%Y Cf. A130783, A131529, A327743.
%K nonn,more
%O 1,2
%A _Peter Kagey_, Sep 27 2019
%E a(11) from _Giovanni Resta_, Sep 29 2019
%E a(12)-a(13) from _Freddy Barrera_, Oct 07 2019
|
