A259452 Number of 5 up, 5 down, 5 up, ... permutations of length 5n+1.

1, 1, 252, 578005, 6190034016, 214265281290061, 19157603395806362772, 3800502511986185228829385, 1498722661993096106927612109936, 1081056808393919319749313795137642521, 1336319624105519211256870506149168604698792

Offset: 0

Author

N. J. A. Sloane, Jun 28 2015

Keywords

• nonn

References

• P. R. Stein, personal communication.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100
• P. R. Stein & N. J. A. Sloane, Correspondence, 1975

Crossrefs

Cf. A005981-A005983.

Programs

Maple

b:= proc(u, o, t) option remember; `if`(u+o=0, 1, add(`if`(
       t=5, b(o-j, u+j-1, 1), b(u+j-1, o-j, t+1)), j=1..o))
    end:
a:= n-> b(0, 5*n+1, 0):
seq(a(n), n=0..10);  # Alois P. Heinz, Jul 02 2015

Mathematica

k = 5; b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, Sum[If[t == k, b[o - j, u + j - 1, 1], b[u + j - 1, o - j, t + 1]], {j, 1, o}]]; Array[b[0, k # + 1, 0] &, 10] (* Michael De Vlieger, Oct 15 2017, after Jean-François Alcover at A005983 *)

Extensions

More terms from Alois P. Heinz, Jul 02 2015