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A126972 Sequence gives the number of distinct values taken by the entropy of a permutation of [1..n], where the "entropy" of a permutation pi is sum((pi(n)-n)^2). +0
1
1, 2, 4, 11, 21, 36, 57, 85, 121, 166, 221, 287, 365, 456, 561, 681, 817, 970, 1141, 1331, 1541, 2025 (list; graph; listen)
OFFSET

1,2

COMMENT

A007290 supplies the last term (highest "permutation entropy"). A000292 yields average of "permutation entropy" : sum((c(n)-n)^2)/n.

FORMULA

Sequence begins 1,2,4, then equals 1 + C(n,3) for n>4.

EXAMPLE

For 24 permutations on elements 1,2,3,4 the set of sum((pi(n)-n)^2) yields 0,2,4,6,8,10,12,14,16,18,20 (11 distinct values).

For 120 permutations on elements 1,2,3,4,5 the set of sum((pi(n)-n)^2) yields 0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,36,38,40 (21 values).

CROSSREFS

Cf. A007920, A000292.

Sequence in context: A076636 A011954 A026275 this_sequence A018774 A102608 A018259

Adjacent sequences: A126969 A126970 A126971 this_sequence A126973 A126974 A126975

KEYWORD

nonn

AUTHOR

Jeff Boscole (jazzerciser(AT)hotmail.com), Mar 20 2007

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Last modified July 23 17:35 EDT 2008. Contains 142285 sequences.


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