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

0,2

Links

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

Formula

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

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

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

Example

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

Mathematica

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

Prog

(PARI) for(n=0, 100, print1(sum(k=1, n, floor(log(3*k+1)/log(2))), ", ")) \\ G. C. Greubel, Sep 09 2018
(Magma) [0] cat [(&+[Floor(Log(3*k+1)/Log(2)) : k in [1..n]]): n in [1..100]]; // G. C. Greubel, Sep 09 2018

Crossrefs

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

Sequence in context: A087160 A336411 A107427 * A276208 A225635 A256967

Adjacent sequences: A130248 A130249 A130250 * A130252 A130253 A130254

Keyword

nonn

Author

Hieronymus Fischer, May 20 2007

Status

approved