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A139351
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Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k's that are even, o(n) the number that are odd; sequence gives e(n).
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13
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0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 3, 2, 3, 1, 2, 1, 2, 2, 3, 2, 3, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 3, 2, 3, 1, 2, 1, 2, 2, 3, 2, 3, 1, 2, 1, 2, 2, 3, 2, 3, 1, 2, 1, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 4, 3, 4, 2, 3, 2, 3, 3, 4, 3, 4, 1, 2, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| e(n)+o(n) = A000120(n), the binary weight of n.
a(n) is also number of 1's and 3's in 4-ary representation of n. [From Frank Ruskey (ruskey(AT)cs.uvic.ca), May 02 2009]
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LINKS
| N. J. A. Sloane, Fortran program for this and related sequences
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
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FORMULA
| G.f.: (1/(1-z))*SUM( z^(4^m)/(1+z^(4^m)), m >= 0 ). [From Frank Ruskey (ruskey(AT)cs.uvic.ca), May 03 2009]
Recurrence relation: a(0)=0, a(4m) = a(4m+2) = a(m), a(4m+1) = a(4m+3) = 1+a(m). [From Frank Ruskey (ruskey(AT)cs.uvic.ca), May 11 2009]
a(n)=Sum_k {A030308(n,k)*A059841(k)}. - From DELEHAM Philippe, Oct 14 2011.
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EXAMPLE
| If n = 43 = 2^0+2^1+2^3+2^5, e(43)=1, o(43)=3.
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PROG
| See link for Fortran program.
(Haskell)
import Data.List (unfoldr)
a139351 = sum . map (`mod` 2) .
unfoldr (\x -> if x == 0 then Nothing else Just (x, x `div` 4)
-- Reinhard Zumkeller, Apr 22 2011
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CROSSREFS
| Cf. A000120, A139352-A139355, A039004, A139370-A139373.
Sequence in context: A070088 A131851 A104886 * A125925 A036578 A077402
Adjacent sequences: A139348 A139349 A139350 * A139352 A139353 A139354
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KEYWORD
| nonn
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AUTHOR
| Nadia Heninger (nadiah(AT)cs.princeton.edu) and N. J. A. Sloane (njas(AT)research.att.com), Jun 07 2008
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EXTENSIONS
| Typo in example fixed by Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 22 2011
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