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A106732
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Expansion of -3*x/(1 - 5*x + 3*x^2).
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2
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0, -3, -15, -66, -285, -1227, -5280, -22719, -97755, -420618, -1809825, -7787271, -33506880, -144172587, -620342295, -2669193714, -11484941685, -49417127283, -212630811360, -914902674951, -3936620940675, -16938396678522, -72882120570585
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: -3*x/(1 - 5*x + 3*x^2).
a(n) = 5*a(n-1) - 3*a(n-2), a(0) = 0, a(1) = -3.
a(n) = -3^((n+1)/2)*ChebyshevU(n-1, 5/(2*sqrt(3))). - G. C. Greubel, Sep 10 2021
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MAPLE
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a[0]:=0: a[1]:=-3: for n from 2 to 22 do a[n]:=5*a[n-1]-3*a[n-2] od: seq(a[n], n=0..30);
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MATHEMATICA
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LinearRecurrence[{5, -3}, {0, -3}, 31] (* G. C. Greubel, Sep 10 2021 *)
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PROG
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(Magma) [n le 2 select -3*(1+(-1)^n)/2 else 5*Self(n-1) - 3*Self(n-2): n in [1..31]]; // G. C. Greubel, Sep 10 2021
(Sage) [-3^((n+1)/2)*chebyshev_U(n-1, 5/(2*sqrt(3))) for n in (0..30)] # G. C. Greubel, Sep 10 2021
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CROSSREFS
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KEYWORD
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sign,easy,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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