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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Andrea G. Amato, Mar 01 2021

Keywords

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.

Examples

			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).

Links

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).

Extensions

a(13)-a(15) from Hugo Pfoertner, Mar 02 2021
a(16) from Hugo Pfoertner, Mar 07 2021
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