A005983 Number of 4 up, 4 down, 4 up, ... permutations of length 4n+1.

1, 1, 70, 26599, 33757360, 107709888805, 726401013530416, 9197888739246870571, 200656681438694771057920, 7065183006232334215872360169, 381446884048286939903298793116160, 30299510478473850351087119774475282895, 3422529682416045761005260546463028151218176

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• P. R. Stein, personal communication.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..132
• P. R. Stein and N. J. A. Sloane, Correspondence, 1975

Crossrefs

Cf. A229885.

Programs

Maple

b:= proc(u, o, t) option remember; `if`(u+o=0, 1, add(`if`(t=4,
      b(o-j, u+j-1, 1), b(u+j-1, o-j, t+1)), j=1..o))
    end:
a:= n-> b(0, 4*n+1, 0):
seq(a(n), n=0..20);  # Alois P. Heinz, Oct 06 2013

Mathematica

b[u_, o_, t_] := b[u, o, t] = If[u+o == 0, 1, Sum[If[t == 4, b[o-j, u+j-1, 1], b[u+j-1, o-j, t+1]], {j, 1, o}]] ; a[n_] := b[0, 4*n+1, 0]; Table[a[n], {n, 1, 20}] (* Jean-François Alcover, Nov 25 2014, after Alois P. Heinz *)

Extensions

Typo in name fixed by Alois P. Heinz, Oct 06 2013