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A106732
Expansion of -3*x/(1 - 5*x + 3*x^2).
2
0, -3, -15, -66, -285, -1227, -5280, -22719, -97755, -420618, -1809825, -7787271, -33506880, -144172587, -620342295, -2669193714, -11484941685, -49417127283, -212630811360, -914902674951, -3936620940675, -16938396678522, -72882120570585
OFFSET
0,2
FORMULA
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*A116415(n-1), n>0.
a(n) = -3^((n+1)/2)*ChebyshevU(n-1, 5/(2*sqrt(3))). - G. C. Greubel, Sep 10 2021
MAPLE
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);
MATHEMATICA
LinearRecurrence[{5, -3}, {0, -3}, 31] (* G. C. Greubel, Sep 10 2021 *)
PROG
(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
CROSSREFS
Cf. A116415.
Sequence in context: A098102 A144067 A001447 * A052981 A086200 A325586
KEYWORD
sign,easy,less
AUTHOR
Roger L. Bagula, May 30 2005
EXTENSIONS
Edited by N. J. A. Sloane, Apr 30 2006
New name by G. C. Greubel, Sep 10 2021
STATUS
approved