A306924 Sum over all partitions of n into distinct parts of the bitwise OR of the parts.

0, 1, 2, 6, 7, 13, 20, 35, 42, 58, 75, 104, 133, 176, 233, 327, 402, 500, 616, 762, 916, 1112, 1329, 1640, 1967, 2350, 2787, 3352, 3960, 4706, 5571, 6706, 7922, 9374, 10982, 12933, 15090, 17578, 20322, 23692, 27391, 31626, 36308, 41788, 47799, 54704, 62258

Offset

0,3

Links

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

Wikipedia, Bitwise operation

Wikipedia, Commutative property

Wikipedia, Identity element

Wikipedia, Partition (number theory)

Wikipedia, Truth table

Maple

b:= proc(n, i, r) option remember; `if`(i*(i+1)/2<n or
      n=0, 0, (t-> `if`(i<n, b(n-i, min(i-1, n-i), t), 0)
      +`if`(i=n, t, 0)+b(n, i-1, r))(Bits[Or](i, r)))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..49);

Crossrefs

Cf. A000009, A066189, A306902, A306923, A306925.

Sequence in context: A078471 A127406 A092310 * A087376 A199974 A176279

Adjacent sequences: A306921 A306922 A306923 * A306925 A306926 A306927

Keyword

nonn,base

Author

Alois P. Heinz, Mar 16 2019

Status

approved