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%I #9 Feb 23 2017 22:14:58
%S 1,17,337,6689,132769,2635313,52307953,1038253121,20608138561,
%T 409048011857,8119135821457,161155572393569,3198754040407009,
%U 63491614090959473,1260236019697968433,25014245551686490241
%N a(n) = 20*a(n-1) - 3*a(n-2).
%C a(n)/a(n-1) tends to (sqrt(97) + 10), an eigenvalue of the matrix and root of the characteristic polynomial x^2 - 20x + 3.
%H G. C. Greubel, <a href="/A136270/b136270.txt">Table of n, a(n) for n = 1..765</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-3).
%F a(n) = 20*a(n-1) - 3*a(n-2), n>2; a(1) = 1, a(2) = 17.
%F [a(3), a(4)] = the 2 X 2 matrix [0,1; -3,20]^n * [1,1].
%F A137246(n) = 20*a(n) - 3*a(n-1), n>4.
%F O.g.f.: (1-3*x)/(1-20*x+3*x^2). - _R. J. Mathar_ and _Alexander R. Povolotsky_, Mar 31 2008
%F a(n) = (1/2)*(10 - sqrt(97))^n - (9/194)*sqrt(97)*(10 + sqrt(97))^n + (1/2)*(10 + sqrt(97))^n + (9/194)*(10 - sqrt(97))^n*sqrt(97) - _Alexander R. Povolotsky_, Mar 31 2008
%e a(4) = 20*a(3) - 3*a(2) = 20*337 - 3*17.
%e [a(3), a(4)] = [0,1; -3,20] ^3 * [1,1] = [337, 6689].
%t LinearRecurrence[{20, -3}, {1, 17}, 50] (* _G. C. Greubel_, Feb 23 2017 *)
%o (PARI) x='x+O('x^50); Vec((1-3*x)/(1-20*x+3*x^2)) \\ _G. C. Greubel_, Feb 23 2017
%Y Cf. A137246.
%K nonn,easy
%O 1,2
%A _Gary W. Adamson_, Mar 19 2008
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