

A373095


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


2



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
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OFFSET

0,17


COMMENTS

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


LINKS



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.


EXAMPLE

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


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}]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



