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 A130252 Partial sums of A130250. 9
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified October 2 02:58 EDT 2023. Contains 365831 sequences. (Running on oeis4.)