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A152163
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a(n)=a(n-1)+a(n-2), n>1 ; a(0)=1, a(1)=-1 .
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7
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1, -1, 0, -1, -1, -2, -3, -5, -8, -13, -21, -34, -55, -89, -144, -233, -377, -610, -987, -1597, -2584, -4181, -6765, -10946, -17711, -28657, -46368, -75025, -121393, -196418, -317811, -514229, -832040, -1346269, -2178309, -3524578, -5702887
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OFFSET
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0,6
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
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G.f.: (1-2*x)/(1-x-x^2).
a(n) = Sum_{k, 0<=k<=n}A147703(n,k)*(-2)^k.
a(n) = -Fibonacci(n-2) for n>=2 .
a(n) = (1/2)*{[(1/2)+(1/2)*sqrt(5)]^n+[(1/2)-(1/2)*sqrt(5)]^n}+(3/10)*sqrt(5)*{[(1/2)-(1/2) *sqrt(5)]^n-[(1/2)+(1/2)*sqrt(5)]^n}, with n>=0 [From Paolo P. Lava, Dec 01 2008]
a(n) = (-1)^n*A039834(n-2). - R. J. Mathar, Mar 22 2011
G.f.: (1/(1-Q(0))-1)*(1-2*x)/x where Q(k)=1 - x^k/(1 - x/( x - x^k/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Feb 23 2013
G.f.: 2 - 2/(Q(0)+1) where Q(k) = 1 - 2*x/(1 - x/(x - 1/Q(k+1) )); (continued fraction ). - Sergei N. Gladkovskii, Apr 05 2013
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MATHEMATICA
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LinearRecurrence[{1, 1}, {1, -1}, 40] (* Harvey P. Dale, Oct 09 2012 *)
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PROG
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(MAGMA) I:=[1, -1]; [n le 2 select I[n] else Self(n-1)+Self(n-2): n in [1..40]]; // Vincenzo Librandi, Feb 23 2013
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CROSSREFS
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Cf. A000045.
Sequence in context: A107358 A185357 A132636 * A039834 A000045 A020695
Adjacent sequences: A152160 A152161 A152162 * A152164 A152165 A152166
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KEYWORD
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easy,sign
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AUTHOR
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Philippe DELEHAM, Nov 27 2008
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STATUS
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approved
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