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A080277 Partial sums of A038712. 20
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

Table of n, a(n) for n=1..58.

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

Klaus Brockhaus, Illustration of A038712 and A080277

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

R. Stephan, Table of generating functions

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

a(1)=1, a(2n) = 2a(n) + 2n, a(2n+1) = 2a(n) + 2n + 1. G.f. 1/(1-x) * sum(k>=0, 2^k*t/(1-t), t=x^2^k). - Ralf Stephan, Sep 07 2003

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

MATHEMATICA

Table[BitXor[n, n-1], {n, 1, 58}] // Accumulate (* Jean-Fran├žois Alcover, Oct 24 2013 *)

CROSSREFS

Cf. A038712, A080333. A001787, A050292, A120385.

Sequence in context: A068719 A191161 A034773 * A047608 A130011 A050022

Adjacent sequences:  A080274 A080275 A080276 * A080278 A080279 A080280

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 19 2003

STATUS

approved

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Last modified July 30 13:12 EDT 2014. Contains 245069 sequences.