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A215488 a(0)=1, a(n) = a(n-1) + a(2*n AND n), where AND is the bitwise AND operator.

%I A215488 #15 Aug 06 2025 17:41:17
%S A215488 1,2,3,6,7,8,15,30,31,32,33,36,67,98,165,330,331,332,333,336,337,338,
%T A215488 345,360,691,1022,1353,1686,2377,3068,5445,10890,10891,10892,10893,
%U A215488 10896,10897,10898,10905,10920,10921,10922,10923,10926,10957,10988,11055,11220,22111,33002
%N A215488 a(0)=1, a(n) = a(n-1) + a(2*n AND n), where AND is the bitwise AND operator.
%H A215488 Robert Israel, <a href="/A215488/b215488.txt">Table of n, a(n) for n = 0..10000</a>
%p A215488 f:= proc(n) option remember;
%p A215488 procname(n-1) + procname(Bits:-And(2*n,n))
%p A215488 end proc:
%p A215488 f(0):= 1:
%p A215488 seq(f(i),i=0..100); # _Robert Israel_, Dec 29 2016
%t A215488 A215488[n_] := A215488[n] = If[n == 0, 1, A215488[n-1] + A215488[BitAnd[2*n, n]]];
%t A215488 Array[A215488, 50, 0] (* _Paolo Xausa_, Aug 06 2025 *)
%o A215488 (Python)
%o A215488 a = [1]*1000
%o A215488 for n in range(1,777):
%o A215488     print(a[n-1], end=', ')
%o A215488     a[n]= a[n-1] + a[2*n & n]
%Y A215488 Cf. A213370.
%K A215488 nonn,base,easy
%O A215488 0,2
%A A215488 _Alex Ratushnyak_, Aug 13 2012