A347060 Total number of 1's in the binary expansion of parts in all partitions of n into distinct parts.

0, 1, 1, 4, 4, 7, 11, 15, 20, 28, 39, 48, 64, 80, 104, 134, 167, 203, 257, 311, 381, 470, 566, 680, 820, 981, 1168, 1394, 1650, 1946, 2300, 2700, 3161, 3705, 4315, 5026, 5845, 6769, 7827, 9049, 10424, 11992, 13784, 15801, 18088, 20702, 23620, 26922, 30665

Offset

0,4

Links

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

Example

a(5) = 7 counts the 1's in [101], [100, 1], [11, 10].

Maple

h:= proc(n) option remember; add(i, i=Bits[Split](n)) end:
b:= proc(n, i) option remember; `if`(n=0, [1, 0],
      `if`(n>i*(i+1)/2, 0, b(n, i-1)+(p-> p+
       [0, p[1]*h(i)])(b(n-i, min(n-i, i-1)))))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=0..60);

Crossrefs

Cf. A000009, A000120, A066189, A066624, A318756, A319140.

Sequence in context: A293678 A063984 A357270 * A211643 A284640 A036605

Adjacent sequences: A347057 A347058 A347059 * A347061 A347062 A347063

Keyword

nonn,base

Author

Alois P. Heinz, Aug 14 2021

Status

approved