Lower bound on cumulative mean of distances between cards after n shuffles in A024222.

Terms

a(0) =0a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =2a(7) =2a(8) =2a(9) =3a(10) =3a(11) =4a(12) =4a(13) =4a(14) =4a(15) =4a(16) =4a(17) =5a(18) =6a(19) =6a(20) =6a(21) =6a(22) =7a(23) =7a(24) =8a(25) =8a(26) =8a(27) =9a(28) =9a(29) =10