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A047992 Number of distinct permutations generated by shuffling n cards with "clump size" <= 2. 3
2, 5, 10, 16, 26, 42, 68, 110, 178, 288, 466, 754, 1220, 1974, 3194 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Take a deck of n cards, cut into two nonempty piles, then do a riffle-shuffle in which no more than 2 consecutive cards fall from the same half. Sequence gives number of distinct n-permutations that result.

LINKS

Table of n, a(n) for n=2..16.

FORMULA

For n>3, a(n) = 2 * F(n+1), with F(n) = A000045(n).

EXAMPLE

a(4)=10 because we can split the deck as 1|234 then shuffle to get 2134 or 2314, or split as 12|34 and get 3421 1324 1342 3124 3142 or split 123|4 and get 1243, 1423. These plus the identity (1234) give 10 permutations in all.

CROSSREFS

Essentially the same as A006355.

Sequence in context: A011903 A078435 A049815 * A079984 A027613 A192701

Adjacent sequences:  A047989 A047990 A047991 * A047993 A047994 A047995

KEYWORD

nonn

AUTHOR

Mike Keith (domnei(AT)aol.com)

STATUS

approved

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Last modified July 25 15:34 EDT 2017. Contains 289795 sequences.