The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A080277 Partial sums of A038712. 23
 1, 4, 5, 12, 13, 16, 17, 32, 33, 36, 37, 44, 45, 48, 49, 80, 81, 84, 85, 92, 93, 96, 97, 112, 113, 116, 117, 124, 125, 128, 129, 192, 193, 196, 197, 204, 205, 208, 209, 224, 225, 228, 229, 236, 237, 240, 241, 272, 273, 276, 277, 284, 285, 288, 289, 304, 305, 308 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS M. J. Bannister, Z. Cheng, W. E. Devanny, and D. Eppstein, Superpatterns and universal point sets, 21st Int. Symp. Graph Drawing, 2013, arXiv:1308.0403 [cs.CG], 2013-2014. M. J. Bannister, Z. Cheng, W. E. Devanny, and D. Eppstein, Superpatterns and universal point sets, Journal of Graph Algorithms and Applications 18(2) (2014), 177-209. Klaus Brockhaus, Illustration of A038712 and A080277. B. Dearden, J. Iiams, and J. Metzger, A Function Related to the Rumor Sequence Conjecture, J. Int. Seq. 14 (2011), #11.2.3. Ralf Stephan, Table of generating functions. [ps file] Ralf Stephan, Table of generating functions. [pdf file] FORMULA a(n) is conjectured to be asymptotic to n*log(n)/log(2). - Klaus Brockhaus, Mar 23 2003 [See Bannister et al., 2013. - N. J. A. Sloane, Nov 26 2013] a(n) = Sum_{k=0..log_2(n)} 2^k*floor(n/2^k). a(2^k) = (k+1)*2^k. a(n) = n + 2*a(floor(n/2)). - Vladeta Jovovic, Aug 06 2003 From Ralf Stephan, Sep 07 2003: (Start) a(1) = 1, a(2*n) = 2*a(n) + 2*n, a(2*n+1) = 2*a(n) + 2*n + 1. G.f.: 1/(1-x) * Sum(k >= 0, 2^k*t/(1-t), t = x^2^k). (End) Product_{n >= 1} (1 + x^(n*2^(n-1)) = (1 + x)*(1 + x^4)*(1 + x^12)*(1 + x^32)*... = 1 + Sum_{n >= 1} x^a(n) = 1 + x + x^4 + x^5 + x^12 + x^13 + .... Hence this sequence lists the numbers representable as a sum of distinct elements of A001787 = [1, 4, 12, ..., n*2^(n-1), ...]. Cf. A050292. See also A120385. - Peter Bala, Feb 02 2013 n log_2 n - 2n < a(n) <= n log_2 n + n [Bannister et al., 2013] - David Eppstein, Aug 31 2013 G.f. A(x) satisfies: A(x) = 2*A(x^2)*(1 + x) + x/(1 - x)^2. - Ilya Gutkovskiy, Oct 30 2019 a(n) = A136013(2n). - Pontus von Brömssen, Sep 06 2020 EXAMPLE From Omar E. Pol, Sep 10 2019: (Start) Illustration of initial terms: a(n) is also the total area (or the total number of cells) in first n regions of an infinite diagram of compositions (ordered partitions) of the positive integers, where the length of the n-th horizontal line segment is equal to A001511(n), the length of the n-th vertical line segment is equal to A006519(n), and area of the n-th region is equal to A038712(n), as shown below (first eight regions): ----------------------------------- n  A038712(n)  a(n)       Diagram ----------------------------------- .                         _ _ _ _ 1      1         1       |_| | | | 2      3         4       |_ _| | | 3      1         5       |_|   | | 4      7        12       |_ _ _| | 5      1        13       |_| |   | 6      3        16       |_ _|   | 7      1        17       |_|     | 8     15        32       |_ _ _ _| . The above diagram represents the eight compositions of 4: [1,1,1,1],[2,1,1],[1,2,1],[3,1],[1,1,2],[2,2],[1,3],[4]. (End) MATHEMATICA Table[BitXor[n, n-1], {n, 1, 58}] // Accumulate (* Jean-François Alcover, Oct 24 2013 *) PROG (PARI) a(n) = fromdigits(Vec(Pol(binary(n<<1))'), 2); \\ Kevin Ryde, Apr 29 2021 CROSSREFS Cf. A001787, A038712, A050292, A080333, A120385. See also A136013, A333979. Sequence in context: A323766 A330223 A325688 * A047608 A266725 A308783 Adjacent sequences:  A080274 A080275 A080276 * A080278 A080279 A080280 KEYWORD nonn AUTHOR N. J. A. Sloane, Mar 19 2003 STATUS approved

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

Last modified August 18 11:47 EDT 2022. Contains 356212 sequences. (Running on oeis4.)