A007346 Order of group generated by perfect shuffles of 2n cards.
2, 8, 24, 24, 1920, 7680, 322560, 64, 92897280, 3715891200, 40874803200, 194641920, 25505877196800, 1428329123020800, 21424936845312000, 160, 23310331287699456000, 1678343852714360832000, 31888533201572855808000
Offset: 1
References
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..200
- Steve Butler, Persi Diaconis and R. L. Graham, The mathematics of the flip and horseshoe shuffles, arXiv:1412.8533 [math.CO], 2014.
- Steve Butler, Persi Diaconis and R. L. Graham, The mathematics of the flip and horseshoe shuffles, The American Mathematical Monthly 123.6 (2016): 542-556.
- P. Diaconis, R. L. Graham and W. M. Kantor, The mathematics of perfect shuffles, Adv. Appl. Math. 4 (2) (1983) 175-196.
- Index entries for sequences related to groups
Programs
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Maple
f:=proc(n) local k,i,np; if n=1 then 2 elif (n mod 2) = 1 then n!*2^(n-1) elif n=6 then 2^9*3*5 elif n=12 then 2^17*3^3*5*11 elif n=2 then 8 elif (n mod 4)=2 then n!*2^n else np:=n; k:=1; for i while (np mod 2) = 0 do np:=np/2; k:=k+1; od; if (n=2^(k-1)) then k*2^k else n!*2^(n-2); fi; fi; end; [seq(f(n),n=1..64)]; # N. J. A. Sloane, Jun 20 2016
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Mathematica
a[1] = 2; a[2] = 8; a[n_] := With[{m = 2^n*n!}, Which[Mod[n, 4] == 2, If[n == 6, m/6, m], Mod[n, 4] == 1, m/2, Mod[n, 4] == 3, m/2, True, If[n == 2^IntegerExponent[n, 2], 2*n*(IntegerExponent[n, 2] + 1), If[n == 12, m/(2*7!), m/4]]]]; Table[a[n], {n, 1, 19}](* Jean-François Alcover, Feb 17 2012, after Franklin T. Adams-Watters *) -
PARI
A007346(n) = local(M); M=2^n*n!; if(n%4==2, if(n==2, 8, if(n==6, M/6, M)), if(n%4==1, if(n==1, 2, M/2), if(n%4==3, M/2, if(n==2^valuation(n, 2), 2*n*(valuation(n, 2)+1), if(n==12, M/(7!*2), M/4))))) \\ Franklin T. Adams-Watters, Nov 30 2006
Formula
See Maple program. - N. J. A. Sloane, Jun 20 2016
Extensions
Corrected and extended by Franklin T. Adams-Watters, Nov 30 2006