This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A007346 Order of group generated by perfect shuffles of 2n cards. (Formerly M1909) 5
 2, 8, 24, 24, 1920, 7680, 322560, 64, 92897280, 3715891200, 40874803200, 194641920, 25505877196800, 1428329123020800, 21424936845312000, 160, 23310331287699456000, 1678343852714360832000, 31888533201572855808000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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, W. M. Kantor, The mathematics of perfect shuffles, Adv. Appl. Math. 4 (2) (1983) 175-196. FORMULA See Maple program. - N. J. A. Sloane, Jun 20 2016 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 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 *) PROG (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 CROSSREFS Cf. A002326, A024222, A274299. Bisections give A002671, A274303. Sequence in context: A072842 A303861 A138387 * A062247 A284951 A171261 Adjacent sequences:  A007343 A007344 A007345 * A007347 A007348 A007349 KEYWORD nonn,nice,easy AUTHOR EXTENSIONS Corrected and extended by Franklin T. Adams-Watters, Nov 30 2006 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 21 14:57 EDT 2018. Contains 316424 sequences. (Running on oeis4.)