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A080776 Oscillating sequence which rises to 2^(k-1) in k-th segment (k>=1) then falls back to 0.

%I A080776 #11 Nov 26 2017 21:49:57
%S A080776 0,0,1,0,1,2,1,0,1,2,3,4,3,2,1,0,1,2,3,4,5,6,7,8,7,6,5,4,3,2,1,0,1,2,
%T A080776 3,4,5,6,7,8,9,10,11,12,13,14,15,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,
%U A080776 1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,31,30
%N A080776 Oscillating sequence which rises to 2^(k-1) in k-th segment (k>=1) then falls back to 0.
%C A080776 k-th segment has length 2^k (k>=0).
%D A080776 Hsien-Kuei Hwang, S Janson, TH Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016; http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf. Also Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585
%H A080776 R. Stephan, <a href="/somedcgf.html">Some divide-and-conquer sequences ...</a>
%H A080776 R. Stephan, <a href="/A079944/a079944.ps">Table of generating functions</a>
%F A080776 G.f.: -1 + 2/(1-x) + 1/(1-x)^2 * (-1 + sum(k>=0, 2t^2(t-1), t=x^2^k)). a(n) = A005942(n+2) - 3(n+1), n>0. - _Ralf Stephan_, Sep 13 2003
%F A080776 a(0)=0, a(2n) = a(n) + a(n-1) + (n==1), a(2n+1) = 2a(n). - _Ralf Stephan_, Oct 20 2003
%Y A080776 Essentially the same as A053646.
%K A080776 nonn
%O A080776 0,6
%A A080776 _N. J. A. Sloane_, Mar 11 2003