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A094650
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An accelerator sequence for Catalan's constant.
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3
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5, -1, 9, -4, 25, -16, 78, -64, 257, -256, 874, -1013, 3034, -3953, 10684, -15229, 38017, -58056, 136338, -219508, 491870, -824737, 1782735, -3083887, 6484514, -11489516, 23652443, -42688039, 86459608, -158270401, 316576903, -585868009, 1160673633
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: (5+4x-12x^2-6x^3+3x^4)/(1+x-4x^2-3x^3+3x^4+x^5).
a(n) = (2*cos(2*Pi/11))^n + (-2*cos(Pi/11))^n + (-2*sin(5*Pi/22))^n +(2*sin(3*Pi/22))^n + (-2*sin(Pi/22))^n.
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MATHEMATICA
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LinearRecurrence[{-1, 4, 3, -3, -1}, {5, -1, 9, -4, 25}, 33] (* Jean-François Alcover, Sep 21 2017 *)
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PROG
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(PARI) Vec((5+4*x-12*x^2-6*x^3+3*x^4)/(1+x-4*x^2-3*x^3+3*x^4+x^5) + O(x^40)) \\ Michel Marcus, Jul 25 2015
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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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