%I #20 Dec 19 2018 18:45:33
%S -1,-1,0,1,1,4,3,5,2,9,7,12,5,13,8,11,3,16,13,23,10,27,17,24,7,25,18,
%T 29,11,26,15,19,4,25,21,38,17,47,30,43,13,48,35,57,22,53,31,40,9,41,
%U 32,55,23,60,37,51,14,47,33,52,19,43,24,29,5,36,31,57,26,73,47
%N a(n) = s(n)*r - s(2^r + n), where s(n) = A002487(n) starting at n = 0 and r = 1 + floor(log_2(n)).
%C The same sequence arises for any integer value r > 1 + floor(log_2(n)).
%C The maximum value of a(n) between n=2^k and n=2^(k+1) is the k-th term of A023619.
%F a(0)=-1; a(1)=-1;
%F a(2n) = a(n) + s(n);
%F a(2n+1) = a(n) + a(n+1) + s(2n+1).
%F a(n) = A156140(n) - A002487(n).
%t s[0] = 0; s[1] = 1; s[n_?EvenQ] := s[n] = s[n/2]; s[n_?OddQ] := s[n] = s[(n + 1)/2] + s[(n - 1)/2];
%t a[0]=-1; a[1]=-1; a[n_?EvenQ] := a[n] = a[n/2]+s[n/2]; a[n_?OddQ] := a[n] = s[(n + 1)/2] + s[(n - 1)/2]+a[(n + 1)/2] + a[(n - 1)/2]
%K sign
%O 0,6
%A _Aubrey Laskowski_, Oct 28 2018