A373095 a(n) = a[n/4] + a[n/8] + a[n/16] + ..., where a(0) = 0, a(1) = 1, and [ ] = floor.

0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 0

Author

Clark Kimberling, May 28 2024

Keywords

• nonn

Comments

Every term is a Fibonacci number (A000045), and every nonnegative Fibonacci number occurs.

Examples

			a(20) = a(5) + a(2) + a(1) = 1 + 0 + 1 = 2.
		

Crossrefs

Cf. A000045, A005187, A072376 (sum starts with a[n/2]), A373096, A373097.

Programs

Mathematica

a[0] = 0; a[1] = 1;
a[n_] := a[n] = Sum[a[Floor[n/2^k]], {k, 2, n}]
Table[a[n], {n, 0, 570}]

Formula

The initial 16 terms (0s and 1s) are followed by 16 twos, then 32 threes, then 64 fives,... . Specifically, for m>=3, there are 2^(m+1) F(m)'s.