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%I #10 Jun 13 2015 00:55:36
%S 56,470,1094,7856,128534,201539,3293081,23435699,53805155,382911281,
%T 6256309475,9809462822,160274811896,1140616029542,2618697452438,
%U 18636292598096,304494582579398,477426555904883,7800575092244921,55513782134933123,127452004956911987
%N Numbers n such that T(n) + T(n+1) + ... + T(n+22) is a square, where T = A000217 (triangular numbers).
%C Positive integers y in the solutions to 2*x^2-23*y^2-529*y-4048 = 0.
%H Colin Barker, <a href="/A257707/b257707.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,48670,-48670,0,0,0,0,-1,1).
%F G.f.: x*(10*x^12 +3*x^11 +66*x^10 +414*x^9 +624*x^8 +6762*x^7 -366022*x^6 -73005*x^5 -120678*x^4 -6762*x^3 -624*x^2 -414*x -56) / ((x -1)*(x^12 -48670*x^6 +1)).
%t LinearRecurrence[{1, 0, 0, 0, 0, 48670, -48670, 0, 0, 0, 0, -1, 1}, {56, 470, 1094, 7856, 128534, 201539, 3293081, 23435699, 53805155, 382911281, 6256309475, 9809462822, 160274811896}, 50] (* _Vincenzo Librandi_, May 05 2015 *)
%o (PARI) Vec(x*(10*x^12 +3*x^11 +66*x^10 +414*x^9 +624*x^8 +6762*x^7 -366022*x^6 -73005*x^5 -120678*x^4 -6762*x^3 -624*x^2 -414*x -56) / ((x -1)*(x^12 -48670*x^6 +1)) + O(x^100))
%Y Cf. A176541, A176542, A000217, A000292, A001110, A077415.
%Y Cf. A116476 (length 11), A257293 (length 13), A257708 (length 25), A257709 (length 27), A257710 (length 37).
%K nonn,easy
%O 1,1
%A _Colin Barker_, May 04 2015
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