A227941 Number of 1 up, 3 down, 5 up, 7 down, ... permutations of [n].

1, 1, 1, 2, 3, 4, 19, 55, 125, 245, 434, 4060, 21186, 81212, 254813, 692678, 1688555, 3776432, 60101767, 511650887, 3089821383, 14824989723, 60057570858, 213302293918, 681247718668, 1992449334436, 5409214694961, 132273848506202, 1692162553490943

Offset: 0

Author

Alois P. Heinz, Oct 03 2013

Keywords

• nonn
• eigen

Examples

			a(2) = 1: 12.
a(3) = 2: 132, 231.
a(4) = 3: 1432, 2431, 3421.
a(5) = 4: 15432, 25431, 35421, 45321.
a(6) = 19: 154326, 164325, 165324, 165423, 254316, 264315, 265314, 265413, 354216, 364215, 365214, 365412, 453216, 463215, 465213, 465312, 563214, 564213, 564312.
a(7) = 55: 1543267, 1643257, ..., 6753124, 6754123.
a(8) = 125: 15432678, 16432578, ..., 78641235, 78651234.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A005408, A229066, A229551, A229892.

Programs

Maple

b:= proc(u, o, t, k) option remember; `if`(u+o=0, 1, add(`if`(t=2*k-1,
       b(o-j, u+j-1, 1, k+1), b(u+j-1, o-j, t+1, k)), j=1..o))
    end:
a:= n-> b(0, n, 0, 1):
seq(a(n), n=0..35);

Mathematica

b[u_, o_, t_, k_] := b[u, o, t, k] = If[u+o == 0, 1, Sum[If[t == 2*k-1, b[o-j, u+j-1, 1, k+1], b[u+j-1, o-j, t+1, k]], {j, 1, o}]];
a[n_] := b[0, n, 0, 1];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Sep 01 2022, after Alois P. Heinz *)