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A122247 Partial sums of A005187. 5
0, 1, 4, 8, 15, 23, 33, 44, 59, 75, 93, 112, 134, 157, 182, 208, 239, 271, 305, 340, 378, 417, 458, 500, 546, 593, 642, 692, 745, 799, 855, 912, 975, 1039, 1105, 1172, 1242, 1313, 1386, 1460, 1538, 1617, 1698, 1780, 1865, 1951, 2039, 2128, 2222, 2317, 2414 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Hsien-Kuei Hwang, Svante Janson and Tsung-Hsi 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. Also first authors' copy, 2016. See example 6.2.

FORMULA

a(n) = Sum_{k=1..n} Sum_{j=0..n} floor(k/2^j).

G.f.: (1/(1-x))*Sum_{k>=0} x^(2^k)/((1-x)*(1-x^(2^k))).

MAPLE

b:= proc(n) option remember; `if`(n=0, 0, b(iquo(n, 2))+n) end:

a:= proc(n) option remember; `if`(n=0, 0, b(n)+a(n-1)) end:

seq(a(n), n=0..50);  # Alois P. Heinz, Jan 25 2022

MATHEMATICA

Accumulate[Table[2n-Count[IntegerDigits[2 n, 2], 1], {n, 0, 70}]] (* Harvey P. Dale, Oct 22 2011 *)

CROSSREFS

Cf. A005187 (first differences).

Sequence in context: A102216 A001182 A264599 * A126255 A267682 A194804

Adjacent sequences:  A122244 A122245 A122246 * A122248 A122249 A122250

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Aug 27 2006

STATUS

approved

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Last modified August 10 06:08 EDT 2022. Contains 356029 sequences. (Running on oeis4.)