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A257940 y-values in the solutions to x^2 + x = 5*y^2 + y.

%I A257940 #35 Sep 08 2022 08:46:12
%S A257940 0,1,52,357,16776,114985,5401852,37024845,1739379600,11921885137,
%T A257940 560074829380,3838809989301,180342355680792,1236084894669817,
%U A257940 58069678454385676,398015497273691805,18698256119956506912,128159754037234091425,6020780400947540840020
%N A257940 y-values in the solutions to x^2 + x = 5*y^2 + y.
%C A257940 Also, numbers k such that 2*k^2 + k*(k+1)/2 is a triangular number. Example: 114985 is a term because 2*114985^2 + 114985*114986/2 = 257114*257115/2. - _Bruno Berselli_, Mar 02 2018
%H A257940 Colin Barker, <a href="/A257940/b257940.txt">Table of n, a(n) for n = 1..798</a>
%H A257940 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,322,-322,-1,1).
%F A257940 a(1) = 0, a(2) = 1, a(3) = 52, a(4) = 357, a(5) = 16776; for n > 5, a(n) = a(n-1) + 322*a(n-2) - 322*a(n-3) - a(n-4) + a(n-5).
%F A257940 a(n) = 322*a(n-2) - a(n-4) + 32.
%F A257940 a(n) = 72*A257939(n-2) + 161*a(n-2) + 52.
%F A257940 G.f.: x^2*(3*x^3+17*x^2-51*x-1) / ((x-1)*(x^2-18*x+1)*(x^2+18*x+1)). - _Colin Barker_, May 14 2015
%t A257940 LinearRecurrence[{1, 322, -322, -1, 1}, {0, 1, 52, 357, 16776}, 30] (* _Vincenzo Librandi_, May 15 2015 *)
%o A257940 (Magma) I:=[0, 1, 52, 357, 16776]; [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 A257940 (PARI) concat(0, Vec((3*x^3+17*x^2-51*x-1)/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)) + O(x^100))) \\ _Colin Barker_, May 14 2015
%Y A257940 Cf. A257939.
%K A257940 nonn,easy
%O A257940 1,3
%A A257940 _Arkadiusz Wesolowski_, May 13 2015