This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A047992 #11 Jul 06 2024 11:54:31 %S A047992 2,5,10,16,26,42,68,110,178,288,466,754,1220,1974,3194,5168,8362, %T A047992 13530,21892,35422,57314,92736,150050,242786,392836,635622,1028458, %U A047992 1664080,2692538,4356618,7049156,11405774,18454930,29860704,48315634,78176338,126491972 %N A047992 Number of distinct permutations generated by shuffling n cards with "clump size" <= 2. %C A047992 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 A047992 For n>3, a(n) = 2 * F(n+1), with F(n) = A000045(n). %e A047992 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 A047992 Essentially the same as A006355. %K A047992 nonn %O A047992 2,1 %A A047992 _Mike Keith_ %E A047992 More terms from _Sean A. Irvine_, May 28 2021