A274305 Order of shuffle group generated by in- and out-horseshoe shuffles of a deck of 2n cards.

2, 12, 120, 32, 3628800, 95040, 87178291200, 80, 6402373705728000, 1216451004088320000, 1124000727777607680000, 310224200866619719680000, 403291461126605635584000000, 152444172305856930250752000000, 265252859812191058636308480000000, 192, 295232799039604140847618609643520000000

Offset: 1

Author

N. J. A. Sloane, Jun 20 2016

Keywords

• nonn

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.

Crossrefs

Cf. A007346, A002326.

Programs

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 *)

Formula

See Maple program.