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A110654
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a(2*k) = k, a(2*k+1) = k+1.
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29
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0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| a(n) = A004526(n+1) = A001057(n)*(-1)^(n+1);
for n>0: a(n) = A008619(n-1);
A110655(n) = a(a(n)), A110656(n) = a(a(a(n)));
a(n) = A109613(n)-A028242(n) = A110660(n)/A028242(n).
a(n) = A001222(A029744(n)). - Reinhard Zumkeller, Feb 16 2006
First differences of quarter-squares: a(n)=A002620(n+1)-A002620(n). [From Reinhard Zumkeller, Aug 06 2009]
a(n) = A007742(n) - A173511(n). [From Reinhard Zumkeller, Feb 20 2010]
a(n) = A000217(n) / A008619(n). [Reinhard Zumkeller, Aug 24 2011]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,1,-1).
Charles R Greathouse IV, Table of n, a(n) for n = 0..10000
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FORMULA
| a(n) = floor(n/2) + n mod 2.
a(n) = a(n-1)+a(n-2)-a(n-3) for n>2, a(2)=a(1)=1, a(0)=0. - Reinhard Zumkeller, May 22 2006
Euler transform of length 2 sequence [ 1, 1]. - Michael Somos Sep 19 2006
G.f.: x/((1-x)*(1-x^2)). a(-1-n)=-a(n). - Michael Somos Sep 19 2006
a(n) = floor[(n+1)/2] = |Sum{m=1..n, Sum{k=1..m, (-1)^k}}| for n >= 0 and |x| is the absolute value of x. - William A. Tedeschi, Mar 21 2008
a(n) = A065033(n), n>0. [From R. J. Mathar, Aug 18 2008]
a(n) = 1/4-(-1)^n/4+n/2, with n>=0 [From Paolo P. Lava, Oct 03 2008]
a(n) = ceil(n/2) = ceiling(n/2) = smallest integer >= n/2. [From M. F. Hasler]
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MAPLE
| a:=n->add(chrem( [n, j], [1, 2] ), j=1..n):seq(a(n), n=0..75); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 08 2009]
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PROG
| (PARI) a(n)=n\2+n%2
(PARI) a(n)=(n+1)\2 /* From M. F. Hasler */
(Other) sage: [floor(n/2) + 1 for n in xrange(-1, 75)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2009]
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CROSSREFS
| Essentially the same sequence as A008619 and A123108.
Sequence in context: A140106 A123108 A008619 * A109728 A157271 A025162
Adjacent sequences: A110651 A110652 A110653 * A110655 A110656 A110657
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KEYWORD
| nonn,easy
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 05 2005
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EXTENSIONS
| Deleted wrong formula, added formula & better PARI code. - M. F. Hasler (www.univ-ag.fr/~mhasler), Nov 17 2008
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