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A114960
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Expansion of (-1+3*x-5*x^2+4*x^3) / ((1-2*x)*(2*x^2-1)*(x-1)^2).
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1
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1, 1, 6, 11, 30, 57, 128, 247, 518, 1013, 2068, 4083, 8242, 16369, 32880, 65519, 131310, 262125, 524780, 1048555, 2098154, 4194281, 8390632, 16777191, 33558502, 67108837, 134225892, 268435427, 536887266, 1073741793
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = 2^n - n - 1 - ((-1)^n - 1)*2^(1/2*n)*sqrt(2)/4.
a(n) = 4*a(n-1) - 3*a(n-2) - 6*a(n-3) + 10*a(n-4) - 4*a(n-5) for n>5. - Colin Barker, May 18 2019
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MATHEMATICA
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CoefficientList[Series[(-1+3x-5x^2+4x^3)/((1-2x)(2x^2-1)(x-1)^2), {x, 0, 40}], x] (* or *) LinearRecurrence[ {4, -3, -6, 10, -4}, {1, 1, 6, 11, 30}, 40] (* Harvey P. Dale, Aug 11 2023 *)
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PROG
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(PARI) Vec(x*(1 - 3*x + 5*x^2 - 4*x^3) / ((1 - x)^2*(1 - 2*x)*(1 - 2*x^2)) + O(x^40)) \\ Colin Barker, May 18 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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