login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A122247 Partial sums of A005187. 2

%I

%S 0,1,4,8,15,23,33,44,59,75,93,112,134,157,182,208,239,271,305,340,378,

%T 417,458,500,546,593,642,692,745,799,855,912,975,1039,1105,1172,1242,

%U 1313,1386,1460,1538,1617,1698,1780,1865,1951,2039,2128,2222,2317,2414

%N Partial sums of A005187.

%D Hsien-Kuei Hwang, S Janson, TH 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; http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf. Also Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585

%F G.f.: (1/(1-x))*Sum{k=0..infinity, x^(2^k)/((1-x)*(1-x^(2^k)))}; a(n)=sum{k=1..n, sum{j=0..n, floor(k/2^j)}};

%t Accumulate[Table[2n-Count[IntegerDigits[2 n,2],1],{n,0,70}]] (* _Harvey P. Dale_, Oct 22 2011 *)

%K easy,nonn

%O 0,3

%A _Paul Barry_, Aug 27 2006

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 12 08:23 EDT 2020. Contains 335657 sequences. (Running on oeis4.)