%I #22 Jan 01 2024 08:32:50
%S 0,-3,-15,-66,-285,-1227,-5280,-22719,-97755,-420618,-1809825,
%T -7787271,-33506880,-144172587,-620342295,-2669193714,-11484941685,
%U -49417127283,-212630811360,-914902674951,-3936620940675,-16938396678522,-72882120570585
%N Expansion of -3*x/(1 - 5*x + 3*x^2).
%H G. C. Greubel, <a href="/A106732/b106732.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-3).
%F G.f.: -3*x/(1 - 5*x + 3*x^2).
%F a(n) = 5*a(n-1) - 3*a(n-2), a(0) = 0, a(1) = -3.
%F a(n) = -3*A116415(n-1), n>0.
%F a(n) = -3^((n+1)/2)*ChebyshevU(n-1, 5/(2*sqrt(3))). - _G. C. Greubel_, Sep 10 2021
%p 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);
%t LinearRecurrence[{5,-3}, {0,-3}, 31] (* _G. C. Greubel_, Sep 10 2021 *)
%o (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
%o (Sage) [-3^((n+1)/2)*chebyshev_U(n-1, 5/(2*sqrt(3))) for n in (0..30)] # _G. C. Greubel_, Sep 10 2021
%Y Cf. A116415.
%K sign,easy,less
%O 0,2
%A _Roger L. Bagula_, May 30 2005
%E Edited by _N. J. A. Sloane_, Apr 30 2006
%E New name by _G. C. Greubel_, Sep 10 2021