A306777 a(0)=0, a(1)=1, a(n) = a(n-1) + sum(a(floor(n/d)), d=2^x, x=1...n).

0, 1, 2, 3, 6, 9, 13, 17, 26, 35, 47, 59, 76, 93, 114, 135, 170, 205, 249, 293, 352, 411, 482, 553, 646, 739, 849, 959, 1094, 1229, 1385, 1541, 1746, 1951, 2191, 2431, 2724, 3017, 3354, 3691, 4102, 4513, 4983, 5453, 6006, 6559, 7183, 7807, 8546, 9285, 10117, 10949

Offset

0,3

Links

Table of n, a(n) for n=0..51.

Example

a(18) = a(17) + a(9) + a(4) + a(2) + a(1) = 205 + 35 + 6 + 2 + 1 = 205.

Prog

(Python)
a = [0]*1000
a[1] = 1
for n in range(2, len(a)):
  a[n] = a[n-1]
  d = 2
  while d <= n:
    a[n] += a[n//d]
    d *= 2
print(a)

Crossrefs

Sequence in context: A248187 A190772 A130673 * A062891 A018599 A325340

Adjacent sequences: A306774 A306775 A306776 * A306778 A306779 A306780

Keyword

nonn

Author

Alex Ratushnyak, Mar 11 2019

Status

approved