A306902 Sum over all partitions of n of the bitwise OR of the parts.

0, 1, 3, 7, 13, 23, 40, 67, 103, 156, 231, 340, 486, 689, 964, 1352, 1845, 2507, 3363, 4500, 5937, 7814, 10174, 13247, 17064, 21930, 27957, 35616, 45009, 56805, 71252, 89320, 111282, 138479, 171421, 212021, 260974, 320837, 392753, 480395, 585239, 712163, 863536

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<1, 0, (t->
      `if`(i<n, b(n-i, min(i, 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..45);

Crossrefs

Cf. A006906, A066186, A306884, A306895, A306901, A306903, A306924.

Sequence in context: A155339 A122886 A154691 * A227121 A078447 A066624

Adjacent sequences: A306899 A306900 A306901 * A306903 A306904 A306905

Keyword

nonn,base

Author

Alois P. Heinz, Mar 15 2019

Status

approved