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 A123753 Partial sums of A070941. 11
 1, 3, 6, 9, 13, 17, 21, 25, 30, 35, 40, 45, 50, 55, 60, 65, 71, 77, 83, 89, 95, 101, 107, 113, 119, 125, 131, 137, 143, 149, 155, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280, 287, 294, 301, 308, 315, 322, 329, 336, 343 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Peter Luschny, Table of n, a(n) for n = 0..10000 Hsien-Kuei Hwang, S. Janson and T.-H. Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint 2016. Hsien-Kuei Hwang, S. Janson and T.-H. Tsai, Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47. FORMULA a(n) = A003314(n+1)+1. - Reinhard Zumkeller, Oct 12 2006 Let bil(n) = floor(log_2(n)) + 1 for n>0, bil(0) = 0 and b(n) = n + n*bil(n) - 2^bil(n) + 1 then a(n) = b(n+1). (This suggests that '0' be prepended to this sequence.) - Peter Luschny, Dec 02 2017 MAPLE A123753 := proc(n) local i, J, z; i := n+1: J := i; i := i-1; z := 1; while 0 <= i do J := J+i; i := i-z; z := z+z od; J end: seq(A123753(n), n=0..57); # Peter Luschny, Nov 30 2017 # Alternatively: a := n -> (n+1)*(1 + ilog2(2*n+3)) - 2^ilog2(2*n+3) + 1: seq(a(n), n=0..57); # Peter Luschny, Dec 02 2017 MATHEMATICA a[n_] := (n + 1)(1 + IntegerLength[n + 1, 2]) - 2^IntegerLength[n + 1, 2] + 1; Table[a[n], {n, 0, 57}] (* Peter Luschny, Dec 02 2017 *) PROG (Python) def A123753(n):     s, i, z = n+1, n, 1     while 0 <= i: s += i; i -= z; z += z     return s print([A123753(n) for n in range(0, 58)]) # Peter Luschny, Nov 30 2017 CROSSREFS Cf. A001855, A003314, A033156, A054248, A061168, A083652, A097383, A295508. Sequence in context: A278449 A006590 A061781 * A124288 A256966 A280944 Adjacent sequences:  A123750 A123751 A123752 * A123754 A123755 A123756 KEYWORD nonn AUTHOR Reinhard Zumkeller, Oct 12 2006 STATUS approved

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Last modified August 8 09:27 EDT 2022. Contains 356005 sequences. (Running on oeis4.)