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A342140
Number of permutations of degree n with greatest sum of distances and highest Shannon entropy.
1
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.
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
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