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A228207 x-values in the solution to x^2 - 20*y^2 = 176.

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%I A228207 #25 Nov 03 2024 06:16:11
%S A228207 14,16,26,34,64,86,166,224,434,586,1136,1534,2974,4016,7786,10514,
%T A228207 20384,27526,53366,72064,139714,188666,365776,493934,957614,1293136,
%U A228207 2507066,3385474,6563584,8863286,17183686,23204384,44987474,60749866,117778736,159045214
%N A228207 x-values in the solution to x^2 - 20*y^2 = 176.
%H A228207 Vincenzo Librandi, <a href="/A228207/b228207.txt">Table of n, a(n) for n = 1..1000</a>
%H A228207 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-1).
%F A228207 G.f.: -2*x*(x-1)*(7*x^2+15*x+7) / ((x^2-x-1)*(x^2+x-1)).
%F A228207 a(n) = 3*a(n-2)-a(n-4).
%F A228207 a(n) = 2*A228210(n). - _Hugo Pfoertner_, Feb 11 2024
%t A228207 CoefficientList[Series[-2 (x - 1) (7 x^2 + 15 x + 7) / ((x^2 - x - 1) (x^2 + x - 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 17 2013 *)
%t A228207 LinearRecurrence[{0,3,0,-1},{14,16,26,34},50] (* _Harvey P. Dale_, May 25 2023 *)
%o A228207 (PARI) Vec(-2*x*(x-1)*(7*x^2+15*x+7)/((x^2-x-1)*(x^2+x-1)) + O(x^100))
%o A228207 (Magma) I:=[14,16,26,34]; [n le 4 select I[n] else 3*Self(n-2)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Aug 17 2013
%Y A228207 Cf. A228208, A228210.
%K A228207 nonn,easy
%O A228207 1,1
%A A228207 _Colin Barker_, Aug 16 2013