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

2, 5, 10, 16, 26, 42, 68, 110, 178, 288, 466, 754, 1220, 1974, 3194, 5168, 8362, 13530, 21892, 35422, 57314, 92736, 150050, 242786, 392836, 635622, 1028458, 1664080, 2692538, 4356618, 7049156, 11405774, 18454930, 29860704, 48315634, 78176338, 126491972

Offset: 2

Author

Mike Keith

Keywords

• nonn

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.

Examples

			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.

Formula

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

Extensions

More terms from Sean A. Irvine, May 28 2021