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A275795 The x members of the positive proper solutions (x = x2(n), y = y2(n)) of the second class for the Pell equation x^2 - 2*y^2 = +7^2.

%I A275795 #18 Sep 01 2022 15:17:23
%S A275795 11,57,331,1929,11243,65529,381931,2226057,12974411,75620409,
%T A275795 440748043,2568867849,14972459051,87265886457,508622859691,
%U A275795 2964471271689,17278204770443,100704757350969,586950339335371,3420997278661257,19939033332632171,116213202717131769
%N A275795 The x members of the positive proper solutions (x = x2(n), y = y2(n)) of the second class for the Pell equation x^2 - 2*y^2 = +7^2.
%C A275795 For details and the Nagell reference see A275793.
%C A275795 The y2(n) members are given in A275795(n).
%H A275795 Colin Barker, <a href="/A275795/b275795.txt">Table of n, a(n) for n = 0..1000</a>
%H A275795 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A275795 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-1).
%F A275795 a(n) = 57*S(n-1,6) - 11*S(n-2,6) with the Chebyshev polynomials S(n, 6) = A001109(n+1), n >= -1, with S(-2, 6) = -1.
%F A275795 O.g.f.: (11 - 9*x)/(1 - 6*x + x^2).
%F A275795 a(n) = 6*a(n-1) - a(n-2), n >= 1, with a(-1) = 9 and a(0) = 11.
%F A275795 a(n) = (((3-2*sqrt(2))^n*(-12+11*sqrt(2))+(3+2*sqrt(2))^n*(12+11*sqrt(2)))) / (2*sqrt(2)). - _Colin Barker_, Sep 28 2016
%t A275795 LinearRecurrence[{6,-1},{11,57},30] (* _Harvey P. Dale_, Sep 01 2022 *)
%o A275795 (PARI) a(n) = round((((3-2*sqrt(2))^n*(-12+11*sqrt(2))+(3+2*sqrt(2))^n*(12+11*sqrt(2)))) / (2*sqrt(2))) \\ _Colin Barker_, Sep 28 2016
%o A275795 (PARI) Vec((11-9*x)/(1-6*x+x^2) + O(x^30)) \\ _Colin Barker_, Oct 09 2016
%Y A275795 Cf. A275793, A275794, A275795.
%K A275795 nonn,easy
%O A275795 0,1
%A A275795 _Wolfdieter Lang_, Sep 27 2016