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A274305 Order of shuffle group generated by in- and out-horseshoe shuffles of a deck of 2n cards. 1
2, 12, 120, 32, 3628800, 95040, 87178291200, 80, 6402373705728000, 1216451004088320000, 1124000727777607680000, 310224200866619719680000, 403291461126605635584000000, 152444172305856930250752000000, 265252859812191058636308480000000, 192, 295232799039604140847618609643520000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Jean-François Alcover, Table of n, a(n) for n = 1..64

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.

FORMULA

See Maple program.

MAPLE

f:=proc(n) local k, i, np;

if n=1 then 2

elif n=2 then 12

elif n=3 then 120

elif n=6 then 12!/7!

elif (n mod 2) = 1 then (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+1)*2^k else (2*n)!/2; fi;

fi;

end;

[seq(f(n), n=1..64)];

MATHEMATICA

a[n_] := Which[n == 1, 2, n == 2, 12, n == 3, 120, n == 6, 12!/7!, OddQ[n], (2 n)!, True, np = n; k = 1; While[EvenQ[np], np = np/2; k++]; If[n == 2^(k - 1), (k + 1)*2^k, (2n)!/2]];

Array[a, 17] (* Jean-François Alcover, Nov 30 2017, from Maple *)

CROSSREFS

Cf. A007346, A002326.

Sequence in context: A009748 A212414 A305051 * A317013 A328857 A295864

Adjacent sequences:  A274302 A274303 A274304 * A274306 A274307 A274308

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 20 2016

STATUS

approved

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Last modified September 25 21:49 EDT 2022. Contains 356986 sequences. (Running on oeis4.)