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

0,3

Comments

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

Links

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

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).

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 *)

Prog

(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
(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

Crossrefs

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

Cf. A001045, A105348.

Sequence in context: A310738 A310739 A310740 * A130254 A278114 A263996

Adjacent sequences: A130249 A130250 A130251 * A130253 A130254 A130255

Keyword

nonn

Author

Hieronymus Fischer, May 20 2007

Status

approved