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1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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LINKS
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Table of n, a(n) for n=0..88.
Tanya Khovanova, Recursive Sequences
M. Somos, Rational Function Multiplicative Coefficients
Eric Weisstein's World of Mathematics, Inverse Tangent
Eric Weisstein's World of Mathematics, Stirling Transform
Wikipedia, Grandi's series
Wikipedia, +/-1-sequence
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
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G.f.: 1/(1+x).
E.g.f.: exp(-x).
D.g.f.: (2^(1-s)-1)*zeta(s).
Linear recurrence: a(0)=1, a(n)=-a(n-1) for n>0 [Jaume Oliver Lafont, Mar 20 2009]
Sum_{0<=k<=n} a(k) = A059841(n) [Jaume Oliver Lafont, Nov 21 2009]
Sum_{k>=0} a(k)/(k+1) = log(2) [Jaume Oliver Lafont, Mar 30 2010]
Euler transform of length 2 sequence [ -1, 1]. - Michael Somos, Mar 21 2011
Moebius transform is length 2 sequence [ -1, 2]. - Michael Somos, Mar 21 2011
a(n) = -b(n) where b(n) = multiplicative with b(2^e) = 1 if e>1, b(p^e) = -1 if p>2 and e>1. - Michael Somos, Mar 21 2011
a(n) = a(-n) = a(n + 2) = cos( n * pi). a(n) = c_2(n) if n>1 where c_k(n) is Ramanujan's sum. - Michael Somos, Mar 21 2011
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EXAMPLE
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1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 + x^10 - x^11 + x^12 + ...
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MAPLE
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A033999 := n->(-1)^n;
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MATHEMATICA
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Table[(-1)^n, {n, 0, 88}]
PadRight[{}, 89, {1, -1}] (* Arkadiusz Wesolowski, Sep 16 2012 *)
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PROG
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(PARI) a(n)=1-2*(n%2) /* Jaume Oliver Lafont, Mar 20 2009 */
(Haskell)
a033999 = (1 -) . (* 2) . (`mod` 2)
a033999_list = cycle [1, -1] -- Reinhard Zumkeller, May 06 2012, Jan 02 2012
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CROSSREFS
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Sequence in context: A143622 A076479 A155040 * A000012 A162511 A157895
Adjacent sequences: A033996 A033997 A033998 * A034000 A034001 A034002
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KEYWORD
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sign,easy
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AUTHOR
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Vasiliy Danilov (danilovv(AT)usa.net) Jun 15 1998
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EXTENSIONS
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Comment on Fibonacci square unit creation fallacy and Mathematica command added by Alonso del Arte, Nov 30 2009
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STATUS
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approved
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