This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A373095 #14 May 30 2024 22:25:58
%S A373095 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 A373095 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 A373095 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5
%N A373095 a(n) = a[n/4] + a[n/8] + a[n/16] + ..., where a(0) = 0, a(1) = 1, and [ ] = floor.
%C A373095 Every term is a Fibonacci number (A000045), and every nonnegative Fibonacci number occurs.
%F A373095 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 A373095 a(20) = a(5) + a(2) + a(1) = 1 + 0 + 1 = 2.
%t A373095 a[0] = 0; a[1] = 1;
%t A373095 a[n_] := a[n] = Sum[a[Floor[n/2^k]], {k, 2, n}]
%t A373095 Table[a[n], {n, 0, 570}]
%Y A373095 Cf. A000045, A005187, A072376 (sum starts with a[n/2]), A373096, A373097.
%K A373095 nonn
%O A373095 0,17
%A A373095 _Clark Kimberling_, May 28 2024