A319142 Total number of binary digits in the partitions of n into odd parts.

1, 2, 5, 7, 12, 19, 26, 36, 52, 71, 92, 124, 158, 204, 265, 331, 413, 522, 641, 791, 976, 1184, 1435, 1741, 2093, 2506, 3005, 3574, 4237, 5030, 5928, 6971, 8202, 9593, 11212, 13087, 15210, 17653, 20472, 23665, 27308, 31488, 36205, 41570, 47701, 54584, 62387

Offset: 1

Author

David S. Newman, Sep 11 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000009, A070939.

Programs

Maple

h:= proc(n) option remember; 1+ilog2(n) end:
b:= proc(n, i) option remember; `if`(n=0, [1, 0],
      `if`(i<1, 0, b(n, i-1-irem(i, 2))+`if`(i::even
       or i>n, 0, (p-> p+[0, p[1]*h(i)])(b(n-i, i)))))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=1..60);  # Alois P. Heinz, Sep 27 2018

Mathematica

h[n_] := h[n] = 1 + Floor@Log[2, n];
b[n_, i_] := b[n, i] = If[n==0, {1, 0}, If[i<1, 0, b[n, i-1-Mod[i, 2]] + If[EvenQ[i] || i>n, 0, Function[p, p + {0, p[[1]] h[i]}][b[n - i, i]]]]];
a[n_] := b[n, n][[2]];
Array[a, 60] (* Jean-François Alcover, Dec 12 2020, after Alois P. Heinz *)