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A047992 Number of distinct permutations generated by shuffling n cards with "clump size" <= 2. 3

%I

%S 2,5,10,16,26,42,68,110,178,288,466,754,1220,1974,3194

%N Number of distinct permutations generated by shuffling n cards with "clump size" <= 2.

%C 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.

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

%e 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.

%Y Essentially the same as A006355.

%K nonn

%O 2,1

%A Mike Keith (domnei(AT)aol.com)

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Last modified January 24 13:24 EST 2020. Contains 331193 sequences. (Running on oeis4.)