A327845 Number of permutations of {1,2,...,n} such that for every k >= 1, the k-th differences are distinct.

1, 2, 4, 12, 40, 132, 428, 1668, 7628, 36924, 199000, 1161824, 7231332

Offset

1,2

Comments

a(n) <= A131529(n).

Links

Table of n, a(n) for n=1..13.

Example

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:
[1,3,4,2,5]
[1,4,3,5,2]
[1,4,5,3,2]
[1,5,2,4,3]
[1,5,3,2,4]
[2,1,4,5,3]
[2,1,5,3,4]
[2,3,5,1,4]
[2,4,1,5,3]
[2,5,4,1,3]
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.

Crossrefs

Cf. A130783, A131529, A327743.

Sequence in context: A126946 A113179 A214761 * A056236 A300652 A028329

Adjacent sequences: A327842 A327843 A327844 * A327846 A327847 A327848

Keyword

nonn,more

Author

Peter Kagey, Sep 27 2019

Extensions

a(11) from Giovanni Resta, Sep 29 2019

a(12)-a(13) from Freddy Barrera, Oct 07 2019

Status

approved