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A105371
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Expansion of (1-x)(1-x+x^2)/(1-3x+4x^2-2x^3+x^4).
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7
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1, 1, 1, 0, -3, -8, -13, -13, 0, 34, 89, 144, 144, 0, -377, -987, -1597, -1597, 0, 4181, 10946, 17711, 17711, 0, -46368, -121393, -196418, -196418, 0, 514229, 1346269, 2178309, 2178309, 0, -5702887, -14930352, -24157817, -24157817, 0, 63245986, 165580141
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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G.f.: (1-2x+2x^2-x^3)/(1-3x+4x^2-2x^3+x^4); a(n)=3*a(n-1)-4*a(n-2)+2*a(n-3)-a(n-4); (1/2+sqrt(5)/2)^n((1/2+sqrt(5)/10)cos(Pi*n/5)+sqrt(1/10-sqrt(5)/50)sin(Pi*n/5))- (sqrt(5)/2-1/2)^n((sqrt(5)/10-1/2)cos(2*Pi*n/5)+sqrt(1/10+sqrt(5)/50)sin(2*Pi*n/5)).
a(5n)=-F(-5n-1), a(5n+1)=a(5n+2)=-F(-5n-2), a(5n+3)=0, a(5n+4)=F(-5n-4). - Michael Somos, Apr 09 2005
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MATHEMATICA
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CoefficientList[Series[(1-x)(1-x+x^2)/(1-3x+4x^2-2x^3+x^4), {x, 0, 60}], x] (* or *) LinearRecurrence[{3, -4, 2, -1}, {1, 1, 1, 0}, 60] (* Harvey P. Dale, Dec 21 2013 *)
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PROG
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(PARI) a(n)=local(m); m=n%5+1; [1, -1, -1, 0, 1][m]*fibonacci(-n-(m<3)) /* Michael Somos, Apr 09 2005 */
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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