A091311 Partial sums of 3^A007814(n).
0, 1, 4, 5, 14, 15, 18, 19, 46, 47, 50, 51, 60, 61, 64, 65, 146, 147, 150, 151, 160, 161, 164, 165, 192, 193, 196, 197, 206, 207, 210, 211, 454, 455, 458, 459, 468, 469, 472, 473, 500, 501, 504, 505, 514, 515, 518, 519, 600, 601, 604, 605, 614, 615, 618, 619
Offset: 0
Programs
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Mathematica
Join[{0},Accumulate[3^IntegerExponent[Range[64],2]]] (* Harvey P. Dale, May 20 2025 *) -
PARI
a(n)=sum(k=1,n,3^valuation(k,2))
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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))
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Python
def A091311(n): return (int(bin(n)[2:],3)<<1)-n # Chai Wah Wu, Jul 07 2022
Formula
Recurrence: a(2n) = 3a(n) + n, a(2n+1) = 3a(n) + n + 1.
G.f.: 1/(1-x) * sum(k>=0, 3^k*t/(1-t^2), t=x^2^k).
a(n) = 2*A005836(n+1) - n.