A130252 Partial sums of A130250.

0, 1, 4, 7, 11, 15, 20, 25, 30, 35, 40, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 259, 267, 275, 283, 291, 299, 307, 315, 323, 331, 339, 347, 355, 363, 371

Offset: 0

Author

Hieronymus Fischer, May 20 2007

Keywords

• nonn

Comments

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000

Crossrefs

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

Cf. A001045, A105348.

Programs

Magma

A001045:= func< n | (2^n - (-1)^n)/3 >;
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 >;
[A130252(n): n in [0..70]]; // G. C. Greubel, Mar 18 2023

Mathematica

A001045[n_]:= (2^n - (-1)^n)/3;
A130252[n_]:= If[n==0, 0, (2*n*Ceiling[Log[2,3*n-1]] - A001045[Ceiling[Log[2,3*n-1]]+1] +1)/2];
Table[A130252[n], {n,0,70}] (* G. C. Greubel, Mar 18 2023 *)

Python

def A130252(n): return n*(m:=(3*n-1).bit_length())-(((1<>1) # Chai Wah Wu, Apr 17 2025

SageMath

def A001045(n): return (2^n - (-1)^n)/3
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
[A130252(n) for n in range(71)] # G. C. Greubel, Mar 18 2023

Formula

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

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

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