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A024542 Lower bound on cumulative mean of distances between cards after n shuffles in A024222. 2
0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 7, 7, 8, 8, 11, 11, 12, 12, 12, 12, 12, 12, 11, 12, 14, 14, 15, 15, 16, 16, 14, 14, 17, 18, 17, 17, 15, 15, 19, 20, 20, 20, 13, 13, 13, 14, 22, 22, 22, 22, 23, 23, 18, 18, 24, 24, 25, 25, 26, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

REFERENCES

Martin Gardner, "Card Shuffles," Mathematical Carnival, chapter 10, pages 123-138. New York: Vintage Books, 1977.

Tim Folger, "Shuffling Into Hyperspace," Discover, 1991 (vol 12, no 1), pages 66-67.

LINKS

Table of n, a(n) for n=1..80.

EXAMPLE

a(6)=2. Without cut, after shuffle 1 (s1), order is 4 1 5 2 6 3; after s2, 2 4 6 1 3 5; after s3, 1 2 3 4 5 6. Mean distances between cards after s1 = 3.4 (17/5), s2 = 2.6 (13/5), s3 = 1 (5/5). 35/15=2.3, cumulative mean distance, so lower bound is 2. (Cuts change number of shuffles required to return cards to original order, in this case from 3 to 4.)

CROSSREFS

Cf. A024222.

Sequence in context: A061392 A048273 A175387 * A209082 A257684 A098424

Adjacent sequences:  A024539 A024540 A024541 * A024543 A024544 A024545

KEYWORD

easy,nonn

AUTHOR

Enoch Haga

STATUS

approved

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Last modified October 18 00:16 EDT 2018. Contains 316297 sequences. (Running on oeis4.)