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A257939 x-values in the solutions to x^2 + x = 5*y^2 + y.

%I A257939 #26 Sep 08 2022 08:46:12
%S A257939 0,2,116,798,37512,257114,12078908,82790070,3889371024,26658145586,
%T A257939 1252365390980,8583840088782,403257766524696,2763969850442378,
%U A257939 129847748455561292,889989708002357094,41810571744924211488,286573922006908542050,13462874254117140538004
%N A257939 x-values in the solutions to x^2 + x = 5*y^2 + y.
%H A257939 Colin Barker, <a href="/A257939/b257939.txt">Table of n, a(n) for n = 1..798</a>
%H A257939 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,322,-322,-1,1).
%F A257939 a(1) = 0, a(2) = 2, a(3) = 116, a(4) = 798, a(5) = 37512; for n > 5, a(n) = a(n-1) + 322*a(n-2) - 322*a(n-3) - a(n-4) + a(n-5).
%F A257939 a(n) = 322*a(n-2) - a(n-4) + 160.
%F A257939 a(n) = 161*a(n-2) + 360*A257940(n-2) + 116.
%F A257939 G.f.: -2*x^2*(3*x^3+19*x^2+57*x+1) / ((x-1)*(x^2-18*x+1)*(x^2+18*x+1)). - _Colin Barker_, May 14 2015
%t A257939 LinearRecurrence[{1, 322, -322, -1, 1}, {0, 2, 116, 798, 37512}, 30] (* _Vincenzo Librandi_, May 15 2015 *)
%o A257939 (Magma) I:=[0, 2, 116, 798, 37512]; [n le 5 select I[n] else Self(n-1)+322*Self(n-2)-322*Self(n-3)-Self(n-4)+Self(n-5): n in [1..19]];
%o A257939 (PARI) concat(0, Vec(-2*(3*x^3+19*x^2+57*x+1)/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)) + O(x^100))) \\ _Colin Barker_, May 14 2015
%Y A257939 Subsequence of A077259.
%Y A257939 Cf. A257940.
%K A257939 nonn,easy
%O A257939 1,2
%A A257939 _Arkadiusz Wesolowski_, May 13 2015