A130252 - OEIS

%I #14 Mar 18 2023 19:12:12

%S 0,1,4,7,11,15,20,25,30,35,40,45,51,57,63,69,75,81,87,93,99,105,112,

%T 119,126,133,140,147,154,161,168,175,182,189,196,203,210,217,224,231,

%U 238,245,252,259,267,275,283,291,299,307,315,323,331,339,347,355,363,371

%N Partial sums of A130250.

%C If the initial zero is omitted, partial sums of A130253.

%H G. C. Greubel, <a href="/A130252/b130252.txt">Table of n, a(n) for n = 0..5000</a>

%F a(n) = Sum_{k=0..n} A130250(k).

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

%F G.f.: (1/(1-x)^2)*Sum_{k>=0} x^A001045(k).

%t A001045[n_]:= (2^n - (-1)^n)/3;

%t A130252[n_]:= If[n==0, 0, (2*n*Ceiling[Log[2,3*n-1]] - A001045[Ceiling[Log[2,3*n-1]]+1] +1)/2];

%t Table[A130252[n], {n,0,70}] (* _G. C. Greubel_, Mar 18 2023 *)

%o (Magma)

%o A001045:= func< n | (2^n - (-1)^n)/3 >;

%o A130252:= func< n | n eq 0 select 0 else (2*n*Ceiling(Log(2, 3*n-1)) - A001045(Ceiling(Log(2,3*n-1)) +1) +1)/2 >;

%o [A130252(n): n in [0..70]]; // _G. C. Greubel_, Mar 18 2023

%o (SageMath)

%o def A001045(n): return (2^n - (-1)^n)/3

%o def A130252(n): return 0 if (n==0) else (2*n*ceil(log(3*n-1,2)) - A001045(ceil(log(3*n-1,2)) +1) +1)/2

%o [A130252(n) for n in range(71)] # _G. C. Greubel_, Mar 18 2023

%Y Cf. A130249, A130251, A130253, A130252, A130234, A130236, A130242, A130244.

%Y Cf. A001045, A105348.

%K nonn

%O 0,3

%A _Hieronymus Fischer_, May 20 2007