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A134250
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Expansion of x*(4+9*x-7*x^2) / ((1-x)*(1+3*x-x^2)).
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2
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4, 1, 7, -14, 55, -173, 580, -1907, 6307, -20822, 68779, -227153, 750244, -2477879, 8183887, -27029534, 89272495, -294847013, 973813540, -3216287627, 10622676427, -35084316902, 115875627139, -382711198313, 1264009222084, -4174738864559, 13788225815767
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = 2 + (2^(-1-n)*((-3-sqrt(13))^n*(-19+5*sqrt(13)) + (-3+sqrt(13))^n*(19+5*sqrt(13)))) / sqrt(13).
a(n) = -2*a(n-1) + 4*a(n-2) - a(n-3) for n>3.
(End)
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MAPLE
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end proc:
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MATHEMATICA
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LinearRecurrence[{-2, 4, -1}, {4, 1, 7}, 30] (* Harvey P. Dale, Aug 15 2015 *)
Rest@ CoefficientList[Series[x (4 + 9 x - 7 x^2)/((1 - x) (1 + 3 x - x^2)), {x, 0, 27}], x] (* Michael De Vlieger, May 16 2017 *)
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PROG
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(PARI) Vec(x*(4+9*x-7*x^2)/((1-x)*(1+3*x-x^2)) + O(x^30)) \\ Colin Barker, May 16 2017
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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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