cp's OEIS Frontend

A275796 One half of the y 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 A275796 #16 Oct 09 2016 04:00:59
%S A275796 3,20,117,682,3975,23168,135033,787030,4587147,26735852,155827965,
%T A275796 908231938,5293563663,30853150040,179825336577,1048098869422,
%U A275796 6108767879955,35604508410308,207518282581893,1209505187081050,7049512839904407
%N A275796 One half of the y 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 A275796 For the x2(n) members see A275795(n).
%C A275796 For details and the Nagell reference see A275793.
%H A275796 Colin Barker, <a href="/A275796/b275796.txt">Table of n, a(n) for n = 0..1000</a>
%H A275796 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A275796 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-1).
%F A275796 a(n) = 20*S(n-1,6) - 3*S(n-2,6), with the Chebyshev polynomials S(n, 6) = A001109(n+1) for n >= -1, with S(-2, 6) = -1.
%F A275796 O.g.f: (3 + 2*x)/(1 - 6*x + x^2).
%F A275796 a(n) = 6*a(n-1) - a(n-2) for n >= 1, with a(-1) = -2 and a(0) = 3.
%F A275796 a(n) = (((3-2*sqrt(2))^n*(-11+6*sqrt(2))+(3+2*sqrt(2))^n*(11+6*sqrt(2)))) / (4*sqrt(2)). - _Colin Barker_, Sep 28 2016
%o A275796 (PARI) a(n) = round((((3-2*sqrt(2))^n*(-11+6*sqrt(2))+(3+2*sqrt(2))^n*(11+6*sqrt(2))))/(4*sqrt(2))) \\ _Colin Barker_, Sep 28 2016
%o A275796 (PARI) Vec((3 + 2*x)/(1 - 6*x + x^2) + O(x^20)) \\ _Felix Fröhlich_, Sep 28 2016
%Y A275796 Cf. A275793, A275794, A275795.
%K A275796 nonn,easy
%O A275796 0,1
%A A275796 _Wolfdieter Lang_, Sep 27 2016