A067590 Number of partitions of n into odious numbers (A000069).

1, 1, 2, 2, 4, 4, 6, 7, 11, 12, 16, 19, 25, 29, 37, 44, 56, 64, 79, 92, 112, 130, 157, 182, 217, 250, 296, 341, 401, 461, 539, 615, 717, 817, 945, 1076, 1240, 1409, 1614, 1830, 2091, 2365, 2692, 3040, 3451, 3885, 4398, 4942, 5581, 6260, 7050, 7896, 8870, 9916

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

N. J. A. Sloane, Transforms

Formula

Euler Transform of characteristic function of A000069.

Maple

h:= proc(n) option remember; `if`(n<1, 0,
     `if`(add(i, i=Bits[Split](n))::odd, n, h(n-1)))
    end:
b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,
      b(n, h(i-1))+b(n-i, h(min(n-i, i))))
    end:
a:= n-> b(n, h(n)):
seq(a(n), n=0..100);  # Alois P. Heinz, Sep 08 2019

Mathematica

f[n_] := f[n] = DigitCount[n, 2][[1]] // OddQ // Boole;
etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d p[d], {d, Divisors[j]}] b[n - j], {j, 1, n}]/n]; b];
a[n_] := etr[f][n];
a /@ Range[0, 100] (* Jean-François Alcover, Nov 23 2020 *)

Crossrefs

Cf. A000069, A067591, A116492.

Sequence in context: A007212 A027595 A261797 * A058686 A339447 A027188

Adjacent sequences: A067587 A067588 A067589 * A067591 A067592 A067593

Keyword

easy,nonn

Author

Naohiro Nomoto, Jan 31 2002

Extensions

a(0) corrected by Alois P. Heinz, Sep 08 2019

Status

approved