A005983 Number of 4 up, 4 down, 4 up, ... permutations of length 4n+1. (Formerly M5347)

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

Offset

0,3

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

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 *)

Crossrefs

Cf. A229885.

Sequence in context: A145410 A177638 A274646 * A200313 A177642 A177644

Adjacent sequences: A005980 A005981 A005982 * A005984 A005985 A005986

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

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

Status

approved