A242391 Number of compositions of n in which each part has odd multiplicity.

1, 1, 1, 4, 3, 10, 16, 28, 49, 91, 186, 266, 670, 884, 2350, 3028, 8259, 10536, 30241, 37382, 108628, 135550, 391202, 503750, 1429838, 1884659, 5222976, 7107138, 19119324, 27088726, 70366026, 103884570, 259884905, 399686188, 962312254, 1543116240, 3576132805

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Example

a(0) = 1: the empty composition.
a(1) = 1: [1].
a(2) = 1: [2].
a(3) = 4: [3], [2,1], [1,2], [1,1,1].
a(4) = 3: [4], [3,1], [1,3].
a(5) = 10: [5], [4,1], [1,4], [3,2], [2,3], [2,1,1,1], [1,2,1,1], [1,1,2,1], [1,1,1,2], [1,1,1,1,1].

Maple

b:= proc(n, i, p) option remember; `if`(n=0, p!,
      `if`(i<1, 0, add(`if`(j=0 or irem(j, 2)=1,
         b(n-i*j, i-1, p+j)/j!, 0), j=0..n/i)))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..45);

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[n==0, p!, If[i<1, 0, Sum[If[j==0 || Mod[j, 2]==1, b[n-i*j, i-1, p+j]/j!, 0], {j, 0, n/i}]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 45}] (* Jean-François Alcover, Feb 08 2017, translated from Maple *)

Crossrefs

Cf. A130495 (for even multiplicity).

Sequence in context: A065763 A185730 A205965 * A241862 A222510 A100492

Adjacent sequences: A242388 A242389 A242390 * A242392 A242393 A242394

Keyword

nonn

Author

Alois P. Heinz, May 12 2014

Status

approved