

A115384


Partial sums of ThueMorse numbers A010060.


20



0, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 6, 7, 8, 8, 9, 9, 9, 10, 10, 11, 12, 12, 12, 13, 14, 14, 15, 15, 15, 16, 17, 17, 17, 18, 18, 19, 20, 20, 20, 21, 22, 22, 23, 23, 23, 24, 24, 25, 26, 26, 27, 27, 27, 28, 29, 29, 29, 30, 30, 31, 32, 32, 33, 33, 33, 34, 34, 35, 36, 36, 36, 37, 38, 38
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000


FORMULA

a(n) = Sum_{k=0..n} A010060(k)^2.
a(n+1) = A115382(2n, n).
a(n)/n > 1/2; a(n) = number of odious numbers <= n, see A000069.  Reinhard Zumkeller, Aug 26 2007, corrected by M. F. Hasler, May 22 2017.
a(n) = Sum_{i=1..n} (S2(n) mod 2), where S2 = binary weight; lim a(n)/n = 1/2. More generally, consider a(n) = Sum_{i=1..n} (F(Sk(n)) mod m), where Sk(n) is sum of digits of n, n in base k; F(t) is an arithmetic function; m integer. How does lim a(n)/n depend on F(t)?  Ctibor O. Zizka, Feb 25 2008
a(n) = n + 1  A159481(n).  Reinhard Zumkeller, Apr 16 2009
a(n) = floor((n+1)/2)+(1+(1)^n)*(1(1)^A000120(n))/4.  Vladimir Shevelev, May 27 2009


MATHEMATICA

Accumulate[Nest[Flatten[#/.{0>{0, 1}, 1>{1, 0}}]&, {0}, 7]] (* Peter J. C. Moses, Apr 15 2013 *)
Accumulate[ThueMorse[Range[0, 100]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 02 2017 *)


PROG

(PARI) a(n)=(n+1)\2(n%2&&hammingweight(n)%2) \\ Charles R Greathouse IV, Mar 22 2013


CROSSREFS

Cf. A010060.
Sequence in context: A125186 A226222 A140473 * A131411 A300068 A194202
Adjacent sequences: A115381 A115382 A115383 * A115385 A115386 A115387


KEYWORD

easy,nonn


AUTHOR

Paul Barry, Jan 21 2006


EXTENSIONS

Edited by M. F. Hasler, May 22 2017


STATUS

approved



