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a(n) = Sum_{k >= 0} floor(n/(4^k)).
2

%I #28 Jul 19 2022 18:23:22

%S 0,1,2,3,5,6,7,8,10,11,12,13,15,16,17,18,21,22,23,24,26,27,28,29,31,

%T 32,33,34,36,37,38,39,42,43,44,45,47,48,49,50,52,53,54,55,57,58,59,60,

%U 63,64,65,66,68,69,70,71,73,74,75,76,78,79,80,81,85,86,87,88,90,91,92,93

%N a(n) = Sum_{k >= 0} floor(n/(4^k)).

%H Reinhard Zumkeller, <a href="/A087069/b087069.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = Sum_{k>=0} A030308(n,k)*A000975(k+1). - _Philippe Deléham_, Oct 16 2011

%F a(n) = A054893(4*n). - _Vaclav Kotesovec_, May 28 2014

%F G.f.: (1/(1 - x))*Sum_{k>=0} x^(4^k)/(1 - x^(4^k)). - _Ilya Gutkovskiy_, Mar 15 2018

%e a(4) = 4 + floor(4/4) + floor(4/16) + floor(4/64) + ... = 5.

%t Table[Sum[Floor[n/4^k], {k, 0, 1000}], {n, 0, 50}] (* _G. C. Greubel_, Oct 11 2017 *)

%o (Haskell)

%o import Data.List (unfoldr)

%o a087069 =

%o sum . unfoldr (\x -> if x == 0 then Nothing else Just (x, x `div` 4))

%o -- _Reinhard Zumkeller_, Apr 22 2011

%o (PARI) for(n=0,50, print1(sum(k=0,1000, floor(n/4^k)), ", ")) \\ _G. C. Greubel_, Oct 11 2017

%Y Cf. A005187, A054893, A242954.

%Y Essentially partial sums of A115362.

%K nonn

%O 0,3

%A _Clark Kimberling_, Aug 07 2003