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%I #10 May 28 2021 17:47:29
%S 2,5,10,16,26,42,68,110,178,288,466,754,1220,1974,3194,5168,8362,
%T 13530,21892,35422,57314,92736,150050,242786,392836,635622,1028458,
%U 1664080,2692538,4356618,7049156,11405774,18454930,29860704,48315634,78176338,126491972
%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)
%E More terms from _Sean A. Irvine_, May 28 2021
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