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