A079945 Partial sums of A079882.

1, 3, 4, 5, 7, 9, 10, 11, 12, 13, 15, 17, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 33, 35, 37, 39, 41, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103

Offset

0,2

References

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

Links

Robert Israel, Table of n, a(n) for n = 0..10000

R. Stephan, Some divide-and-conquer sequences ...

R. Stephan, Table of generating functions

Formula

See A080596 for an explicit formula.

a(n) = (3*n+3-2^(A000523((n+2)/2))-(-1)^A079944(n)*(n+3-3*2^(A000523((n+2)/2))))/2. - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 23 2003

Also a(n) = n+2^A000523((n+2)/2)*(1-3*A079944(n))+A079944(n)*(n+3) - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 23 2003

Maple

A079882:= [seq(op([1$(2^n), 2$(2^n)]), n=0..6)]:
ListTools:-PartialSums(A079882); # Robert Israel, Oct 26 2020

Crossrefs

Apart from initial terms, same as A080596.

Sequence in context: A162610 A155935 A081606 * A283736 A039017 A275319

Adjacent sequences: A079942 A079943 A079944 * A079946 A079947 A079948

Keyword

nonn,look

Author

N. J. A. Sloane, Feb 21 2003

Status

approved