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

Author

Alois P. Heinz, May 12 2014

Keywords

• nonn

Examples

			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].
		

Links

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

Crossrefs

Cf. A130495 (for even multiplicity).

Programs

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 *)