The OEIS is supported by the many generous donors to the OEIS Foundation.

a(n) = a[n/4] + a[n/8] + a[n/16] + ..., where a(0) = 0, a(1) = 1, and [ ] = floor.
2

%I #14 May 30 2024 22:25:58

%S 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,

%T 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,

%U 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5

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

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

%F 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.

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

%t a[0] = 0; a[1] = 1;

%t a[n_] := a[n] = Sum[a[Floor[n/2^k]], {k, 2, n}]

%t Table[a[n], {n, 0, 570}]

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

%K nonn

%O 0,17

%A _Clark Kimberling_, May 28 2024

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 20 16:50 EDT 2024. Contains 376075 sequences. (Running on oeis4.)