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A142888
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First differences of A142705.
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2
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3, -1, 13, -9, 29, -23, 51, -43, 79, -69, 113, -101, 153, -139, 199, -183, 251, -233, 309, -289, 373, -351, 443, -419, 519, -493, 601, -573, 689, -659, 783, -751, 883, -849, 989, -953, 1101, -1063, 1219, -1179, 1343, -1301, 1473, -1429, 1609, -1563, 1751
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OFFSET
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1,1
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COMMENTS
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Also obtained from A135370 if adjacent pairs are swapped and if the sequence is then multiplied by (-1)^(n+1).
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LINKS
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FORMULA
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a(n) = -a(n-1) +2*a(n-2) +2*a(n-3) -a(n-4) -a(n-5). - R. J. Mathar, Sep 12 2010
G.f.: x(3+2x+6x^2-x^4)/((1+x)^3*(1-x)^2). - R. J. Mathar, Oct 24 2008, parenthesis added Sep 12 2010
a(n) = (5+3*(-1)^n+(10-6*(-1)^n)*n-6*(-1)^n*n^2)/8.
a(n) = (-3*n^2+2*n+4)/4 for n even.
a(n) = (3*n^2+8*n+1)/4 for n odd.
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MATHEMATICA
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CoefficientList[Series[(3 + 2 x + 6 x^2 - x^4)/((1 + x)^3 (1 - x)^2), {x, 0, 60}], x] (* Vincenzo Librandi, May 25 2014 *)
LinearRecurrence[{-1, 2, 2, -1, -1}, {3, -1, 13, -9, 29}, 50] (* Harvey P. Dale, Apr 02 2018 *)
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PROG
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(PARI) Vec(x*(3+2*x+6*x^2-x^4)/((1+x)^3*(1-x)^2) + O(x^100)) \\ Colin Barker, Jan 26 2016
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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