A342140 Number of permutations of degree n with greatest sum of distances and highest Shannon entropy.

1, 1, 3, 2, 17, 4, 86, 4, 488, 12, 3172, 40, 22912, 56, 166814, 256

Offset

1,3

Comments

Starting from a list of n ordered numbers, the sequence gives the number of permutations of the list that display both the greatest sum of distances (see A007590 and A062870) and the highest Shannon entropy (see A341838 for a more in-depth explanation on how to calculate it).

A way to interpret this is to see these permutations as the ones with both the highest level of disorder and the greatest distance from a starting configuration.

Links

Table of n, a(n) for n=1..16.

Andrea G. Amato How well can you shuffle a deck of cards?

Andrea G. Amato, Conjectures and properties

Example

Starting from (1,2,3,4), there are only two permutations that have both the greatest sum of distances (which is 8 for n=4) and the highest Shannon entropy (which is 1.039720... for n=4). These permutations are (3,4,2,1) and (4,3,1,2).

Crossrefs

Cf. A007590 (greatest sum of distances of a given n).

Cf. A062870 (permutations that possess this property).

Cf. A341838 (number of permutations with the highest Shannon entropy).

Sequence in context: A209600 A072045 A189731 * A126354 A361084 A158939

Adjacent sequences: A342137 A342138 A342139 * A342141 A342142 A342143

Keyword

nonn,hard,more

Author

Andrea G. Amato, Mar 01 2021

Extensions

a(13)-a(15) from Hugo Pfoertner, Mar 02 2021

a(16) from Hugo Pfoertner, Mar 07 2021

Status

approved