A130251 Partial sums of A130249.

0, 2, 4, 7, 10, 14, 18, 22, 26, 30, 34, 39, 44, 49, 54, 59, 64, 69, 74, 79, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 223, 230, 237, 244, 251, 258, 265, 272, 279, 286, 293, 300, 307, 314, 321

Offset: 0

Author

Hieronymus Fischer, May 20 2007

Keywords

• nonn

Examples

			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
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2500

Crossrefs

Cf. A130249, A130250, A130252, A130253, A130233, A130235, A130241, A130244. Also A105348, A001045.

Programs

Magma

[0] cat [(&+[Floor(Log(3*k+1)/Log(2)) : k in [1..n]]): n in [1..100]]; // G. C. Greubel, Sep 09 2018

Mathematica

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

PARI

for(n=0,100, print1(sum(k=1,n, floor(log(3*k+1)/log(2))), ", ")) \\ G. C. Greubel, Sep 09 2018

Python

def A130251(n): return (n+1)*((m:=(3*n+1).bit_length())-1)-(((1<>1) # Chai Wah Wu, Apr 17 2025

Formula

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

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

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