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Search: id:A152163
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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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+0
8
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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
(list; graph; listen)
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OFFSET
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0,6
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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 (ppl(AT)spl.at), Dec 01 2008]
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CROSSREFS
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Cf. A000045
Sequence in context: A000044 A107358 A132636 this_sequence A039834 A000045 A020695
Adjacent sequences: A152160 A152161 A152162 this_sequence 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 (kolotoko(AT)wanadoo.fr), Nov 27 2008
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