A361257 a(n) = Sum_{j=0..n} n^wt(j), where wt = A000120.

1, 2, 5, 16, 29, 66, 127, 512, 737, 1090, 1541, 3312, 4369, 7658, 12209, 65536, 83537, 105282, 130987, 167600, 203701, 254122, 313259, 649728, 766201, 912626, 1079027, 1778896, 2071469, 3081570, 4329151, 33554432, 39135425, 45436546, 52524221, 60511536

Offset: 0

Author

Alois P. Heinz, Mar 06 2023

Keywords

• nonn
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..16382

Crossrefs

Cf. A000120, A002416, A059841, A360189.

Programs

Maple

b:= proc(n) option remember; `if`(n<0, 0,
      b(n-1)+x^add(i, i=Bits[Split](n)))
    end:
a:= n-> subs(x=n, b(n)):
seq(a(n), n=0..37);

Python

def A361257(n): return sum([n**j.bit_count() for j in range(0,n+1)])
print(list(A361257(n) for n in range(0,37))) # Dumitru Damian, Mar 06 2023

Python

from collections import Counter
def A361257(n): return sum(j*n**i for i, j in Counter(j.bit_count() for j in range(n+1)).items()) # Chai Wah Wu, Mar 06 2023

Formula

a(n) = Sum_{j=0..n} n^wt(j), where wt = A000120.

a(n) = Sum_{k>=0} n^k * A360189(n,k).

a(n) mod 2 = A059841(n).

a(2^n-1) = 2^(n^2) = A002416(n).