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

1,2

Links

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

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 *)

Crossrefs

Cf. A000009, A070939.

Sequence in context: A005895 A238661 A135525 * A350497 A117538 A001060

Adjacent sequences: A319139 A319140 A319141 * A319143 A319144 A319145

Keyword

nonn

Author

David S. Newman, Sep 11 2018

Status

approved