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A049039
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Geometric Connell sequence: 1 odd, 2 even, 4 odd, 8 even, ...
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7
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1, 2, 4, 5, 7, 9, 11, 12, 14, 16, 18, 20, 22, 24, 26, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 121, 123, 125
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Reinhard Zumkeller, Rows n=1..13 of triangle, flattened
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
| a(n) = 2n-1-floor(log_2(n)). a(2^n-1) = 2^(n+1)-(n+2), the Eulerian numbers
a(0)=0, a(2n) = a(n) + 2n - 1, a(2n+1) = a(n) + 2n + 1. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 11 2003
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MAPLE
| Digits := 100: [seq(2*n-1-floor(evalf(log(n)/log(2))), n=1..100)];
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MATHEMATICA
| a[0] = 0; a[n_?EvenQ] := a[n] = a[n/2]+n-1; a[n_?OddQ] := a[n] = a[(n-1)/2]+n; Table[a[n], {n, 1, 100}] (* From Jean-François Alcover, Dec 27 2011, after Ralf Stephan *)
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PROG
| (Haskell)
a049039 n k = a049039_tabl !! (n-1) !! (k-1)
a049039_row n = a049039_tabl !! (n-1)
a049039_tabl = f 1 1 [1..] where
f k p xs = ys : f (2 * k) (1 - p) (dropWhile (<= last ys) xs) where
ys = take k $ filter ((== p) . (`mod` 2)) xs
-- Reinhard Zumkeller, Jan 18 2012, Jul 08 2011
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CROSSREFS
| Cf. A001614, A033292, A030196, A000295, A050487, A050488.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009: (Start)
Cf. A160464, A160465 and A160473.
(End)
Sequence in context: A083026 A047379 A093848 * A005152 A060831 A073727
Adjacent sequences: A049036 A049037 A049038 * A049040 A049041 A049042
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KEYWORD
| easy,nonn,nice,tabf
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AUTHOR
| James A. Sellers (sellersj(AT)math.psu.edu)
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EXTENSIONS
| Keyword tabf added by Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 22 2012
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