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A078043
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Expansion of (1-x)/(1+x-x^2+2*x^3).
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2
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1, -2, 3, -7, 14, -27, 55, -110, 219, -439, 878, -1755, 3511, -7022, 14043, -28087, 56174, -112347, 224695, -449390, 898779, -1797559, 3595118, -7190235, 14380471, -28760942, 57521883, -115043767, 230087534, -460175067, 920350135, -1840700270, 3681400539, -7362801079
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| ABS(a(n)) = A033129(n+1) - A033129(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 22 2010]
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FORMULA
| a(0)=1, a(1)=-2, a(2)=3, a(n)=a(n-1)+a(n-2)-2*a(n-3) [From Harvey P. Dale, Feb 02 2012]
a(n)=1/21*(-9*2^n*E^(I*n*Pi)+9*Cos[(n*Pi)/3]-Sqrt(3)*Sin((n*Pi)/3]) [From Harvey P. Dale, Feb 02 2012]
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MATHEMATICA
| CoefficientList[Series[(1-x)/(1+x-x^2+2x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{-1, 1, -2}, {1, -2, 3}, 40] (* From Harvey P. Dale, Feb 02 2012 *)
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CROSSREFS
| Sequence in context: A054194 A138651 A131300 * A131666 A135258 A034065
Adjacent sequences: A078040 A078041 A078042 * A078044 A078045 A078046
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KEYWORD
| sign,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2002
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