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%I #8 Jun 13 2015 00:55:36
%S 25,55,208,382,1273,2287,7480,13390,43657,78103,254512,455278,1483465,
%T 2653615,8646328,15466462,50394553,90145207,293721040,525404830,
%U 1711931737,3062283823,9977869432,17848298158,58155284905,104027505175,338953840048,606316732942
%N Numbers n such that T(n) + T(n+1) + ... + T(n+24) is a square, where T = A000217 (triangular numbers).
%C Positive integers y in the solutions to 2*x^2-25*y^2-625*y-5200 = 0.
%H Colin Barker, <a href="/A257708/b257708.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-6,-1,1).
%F G.f.: x*(x^2+4*x+5)*(2*x^2-2*x-5) / ((x-1)*(x^2-2*x-1)*(x^2+2*x-1)).
%t LinearRecurrence[{1, 6, -6, -1, 1}, {25, 55, 208, 382, 1273}, 50] (* _Vincenzo Librandi_, May 05 2015 *)
%o (PARI) Vec(x*(x^2+4*x+5)*(2*x^2-2*x-5)/((x-1)*(x^2-2*x-1)*(x^2+2*x-1)) + O(x^100))
%Y Cf. A176541, A176542, A000217, A000292, A001110, A077415.
%Y Cf. A116476 (length 11), A257293 (length 13), A257707 (length 23), A257709 (length 27), A257710 (length 37).
%K nonn,easy
%O 1,1
%A _Colin Barker_, May 04 2015
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