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A130251
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Partial sums of A130249.
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11
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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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)}.
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EXAMPLE
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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
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MATHEMATICA
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Join[{0}, Table[Sum[Floor[Log[2, 3*k + 1]], {k, 1, n}], {n, 1, 2500}]] (* G. C. Greubel, Sep 09 2018 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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