This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A091311 #14 May 20 2025 15:49:36
%S A091311 0,1,4,5,14,15,18,19,46,47,50,51,60,61,64,65,146,147,150,151,160,161,
%T A091311 164,165,192,193,196,197,206,207,210,211,454,455,458,459,468,469,472,
%U A091311 473,500,501,504,505,514,515,518,519,600,601,604,605,614,615,618,619
%N A091311 Partial sums of 3^A007814(n).
%F A091311 Recurrence: a(2n) = 3a(n) + n, a(2n+1) = 3a(n) + n + 1.
%F A091311 G.f.: 1/(1-x) * sum(k>=0, 3^k*t/(1-t^2), t=x^2^k).
%F A091311 a(n) = 2*A005836(n+1) - n.
%t A091311 Join[{0},Accumulate[3^IntegerExponent[Range[64],2]]] (* _Harvey P. Dale_, May 20 2025 *)
%o A091311 (PARI) a(n)=sum(k=1,n,3^valuation(k,2))
%o A091311 (PARI) a(n)=if(n<1,0,if(n%2==0,3*a(n/2)+n/2,3*a((n-1)/2)+(n+1)/2))
%o A091311 (Python)
%o A091311 def A091311(n): return (int(bin(n)[2:],3)<<1)-n # _Chai Wah Wu_, Jul 07 2022
%Y A091311 First differences are A061393(n)-1.
%Y A091311 Cf. A005836.
%K A091311 nonn,easy
%O A091311 0,3
%A A091311 _Ralf Stephan_, Feb 24 2004