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a(0) = 0; a(1) = 1; a(2*n) = a(n), a(2*n+1) = a(n-a(n)) + a(n-a(n+1)).
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%I #5 May 26 2017 16:44:55

%S 0,1,1,0,1,2,0,1,1,1,2,2,0,2,1,0,1,2,1,2,2,2,2,3,0,2,2,2,1,3,0,1,1,1,

%T 2,1,1,3,2,4,2,2,2,4,2,4,3,5,0,2,2,6,2,0,2,4,1,4,3,5,0,3,1,0,1,2,1,2,

%U 2,2,1,4,1,2,3,3,2,3,4,4,2,4,2,8,2,4,4,6,2,4,4,4,3,6,5,7,0,3,2,10,2

%N a(0) = 0; a(1) = 1; a(2*n) = a(n), a(2*n+1) = a(n-a(n)) + a(n-a(n+1)).

%C A variation on Hofstadter's Q-sequence and Stern's diatomic sequence.

%H Michael Gilleland, <a href="/selfsimilar.html">Some Self-Similar Integer Sequences</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SternsDiatomicSeries.html">Stern's Diatomic Series</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HofstadtersQ-Sequence.html">Hofstadter's Q-Sequence</a>

%H <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>

%H <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>

%t a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], a[(n - 1)/2 - a[(n - 1)/2]] + a[(n - 1)/2 - a[(n + 1)/2]]]; Table[a[n], {n, 0, 100}]

%Y Cf. A002487, A005185, A287476, A287477.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, May 25 2017