%I #22 Jul 20 2023 07:01:35

%S 0,1,1,3,2,5,4,7,3,6,9,9,8,12,11,15,10,14,13,13,12,16,16,20,14,19,23,

%T 23,22,27,26,31,24,24,29,34,33,27,32,37,36,30,35,40,39,39,44,44,42,42,

%U 47,46,45,51,50,56,48,54,60,59,58,64,63,69,55,61,60,66,65,58,64,70,62,68

%N a(0)=0; for n >= 1, a(n) = a(n-1-A023416(n)) + A000120(n).

%H Amiram Eldar, <a href="/A297208/b297208.txt">Table of n, a(n) for n = 0..10000</a>

%H B. Balamohan, A. Kuznetsov and S. Tanny, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Tanny/tanny3.html">On the behavior of a variant of Hofstadter's Q-sequence</a>, J. Integer Sequences, Vol. 10 (2007), Article 07.7.1.

%H Nathaniel D. Emerson, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL9/Emerson/emerson6.html">A Family of Meta-Fibonacci Sequences Defined by Variable-Order Recursions</a>, J. Integer Sequences, Vol. 9 (2006), Article 06.1.8.

%e For n = 7, A023416(7) = 0, A000120(7) = 3 so a(7) = a(6) + 3 , a(6) = a(4) + 2, a(4) = a(1) + 1 , a(1) = a(0) + 1 , a(0) = 0. Thus a(7)= 0 + 1 + 1 + 2 + 3 = 7.

%t a[0] = 0; a[n_] := a[n] = a[n - 1 - DigitCount[n, 2, 0]] + DigitCount[n, 2, 1]; Array[a, 100, 0] (* _Amiram Eldar_, Jul 20 2023 *)

%o (PARI) a(n) = if (n==0, 0, a(n-1-#binary(n)+hammingweight(n)) + hammingweight(n)); \\ _Michel Marcus_, Dec 27 2017

%Y Cf. A023416, A000120.

%K nonn,base

%O 0,4

%A _Ctibor O. Zizka_, Dec 27 2017