%I #13 Sep 08 2022 08:45:30

%S 0,2,4,7,10,14,18,22,26,30,34,39,44,49,54,59,64,69,74,79,84,90,96,102,

%T 108,114,120,126,132,138,144,150,156,162,168,174,180,186,192,198,204,

%U 210,216,223,230,237,244,251,258,265,272,279,286,293,300,307,314,321

%N Partial sums of A130249.

%H G. C. Greubel, <a href="/A130251/b130251.txt">Table of n, a(n) for n = 0..2500</a>

%F a(n) = Sum_{k=0..n} A130249(k).

%F a(n) = (n+1)*floor(log_2(3n+1)) - 1/2*A001045(floor(log_2(3n+1))+2)-1).

%F G.f.: 1/(1-x)^2*Sum{k>=1, x^A001045(k)}.

%e G.f. = 2*x + 4*x^2 + 7*x^3 + 10*x^4 + 14*x^5 + 18*x^6 + 22*x^7 + ... - _Michael Somos_, Sep 17 2018

%t Join[{0}, Table[Sum[Floor[Log[2, 3*k + 1]], {k, 1, n}], {n, 1, 2500}]] (* _G. C. Greubel_, Sep 09 2018 *)

%o (PARI) for(n=0,100, print1(sum(k=1,n, floor(log(3*k+1)/log(2))), ", ")) \\ _G. C. Greubel_, Sep 09 2018

%o (Magma) [0] cat [(&+[Floor(Log(3*k+1)/Log(2)) : k in [1..n]]): n in [1..100]]; // _G. C. Greubel_, Sep 09 2018

%Y Cf. A130250, A130252, A130253, A130233, A130235, A130241, A130244. Also A105348, A001045.

%K nonn

%O 0,2

%A _Hieronymus Fischer_, May 20 2007