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%I #11 Oct 21 2022 22:06:18
%S 2,25,627,15700,393127,9843875,246490002,6172093925,154548838127,
%T 3869893047100,96901875015627,2426416768437775,60757321085960002,
%U 1521359443917437825,38094743419021905627,953889944919465078500,23885343366405648868127,598087474105060686781675,14976072195992922818410002
%N a(n) = 25*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 25.
%H G. C. Greubel, <a href="/A330767/b330767.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (25,1).
%F a(n) = ( (25 + sqrt(629))^n + (25 - sqrt(629))^n )/2^n.
%F G.f.: (2 - 25*x)/(1-25*x-x^2).
%F a(n) = Lucas(n, 25) = 2*(-i)^n * ChebyshevT(n, 25*i/2).
%p seq(simplify(2*(-I)^n*ChebyshevT(n, 25*I/2)), n = 0..25);
%t LucasL[Range[25] -1, 25]
%o (PARI) vector(26, n, 2*(-I)^(n-1)*polchebyshev(n-1, 1, 25*I/2) )
%o (Magma) I:=[2,25]; [n le 2 select I[n] else 25*Self(n-1) +Self(n-2): n in [1..25]];
%o (Sage) [2*(-I)^n*chebyshev_T(n, 25*I/2) for n in (0..25)]
%o (GAP) a:=[2,25];; for n in [3..25] do a[n]:=25*a[n-1]+a[n-2]; od; a;
%Y Lucas polynomials Lucas(n,m): A000032 (m=1), A002203 (m=2), A006497 (m=3), A014448 (m=4), A087130 (m=5), A085447 (m=6), A086902 (m=7), A086594 (m=8), A087798 (m=9), A086927 (m=10), A001946 (m=11), A086928 (m=12), A088316 (m=13), A090300 (m=14), A090301 (m=15), A090305 (m=16), A090306 (m=17), A090307 (m=18), A090308 (m=19), A090309 (m=20), A090310 (m=21), A090313 (m=22), A090314 (m=23), A090316 (m=24), this sequence (m=25).
%K nonn,easy
%O 0,1
%A _G. C. Greubel_, Dec 29 2019
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