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 A145865 #11 Dec 21 2016 08:11:01
%S A145865 0,1,1,0,1,1,0,-1,1,0,1,1,0,1,-1,-2,1,1,0,-1,1,0,1,1,0,-1,1,2,-1,1,-2,
%T A145865 -3,1,0,1,1,0,1,-1,-2,1,1,0,-1,1,0,1,1,0,1,-1,-2,1,-1,2,3,-1,-2,1,3,
%U A145865 -2,1,-3,-4,1,1,0,-1,1,0,1,1,0,-1,1,2,-1,1,-2,-3,1,0,1,1,0,1,-1,-2,1,1,0
%N A145865 a(0) = 0, a(1) = 1, a(2n) = a(n), a(2n+1) = a(n) - a(n+1).
%C A145865 Variation on Stern's Diatomic Series
%H A145865 Michael De Vlieger, <a href="/A145865/b145865.txt">Table of n, a(n) for n = 0..10000</a>
%F A145865 From _Chai Wah Wu_, Dec 20 2016: (Start)
%F A145865 a(2^k*n+1) = a(n+1) if k is even
%F A145865 a(2^k*n+1) = a(n)-a(n+1) = a(2n+1) if k is odd
%F A145865 a(2^k*n+2^k-1) = a(n) - k*a(n+1)
%F A145865 a(2^k*n+2^k-3) = a(n+1) for k >= 2
%F A145865 a(2^k*n+2^k-5) = (k-1)*a(n+1)-a(n) for k >= 3
%F A145865 a(2^k*n+2^k-7) = a(n) - (k-2)*a(n+1) for k >= 3
%F A145865 This implies that
%F A145865 a(2^k+1) = 1 if k is even
%F A145865 a(2^k+1) = 0 if k is odd
%F A145865 a(2^k-1) = 2 - k for k >= 1
%F A145865 a(2^k-3) = 1 for k >= 2
%F A145865 a(2^k-5) = k - 3 for k >= 3
%F A145865 a(2^k-7) = 4 - k for k >= 3
%F A145865 (End)
%t A145865 a[0] = 0; a[1] = 1; a[n_] := a[n] = If[EvenQ@ n, a[n/2], a[#] - a[# + 1] &[(n - 1)/2]]; Table[a@ n, {n, 0, 85}] (* _Michael De Vlieger_, Dec 21 2016 *)
%Y A145865 Cf. A002487, A005590.
%K A145865 easy,sign
%O A145865 0,16
%A A145865 _Paolo P. Lava_ and _Giorgio Balzarotti_, Oct 22 2008