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%I #33 Mar 06 2022 09:02:06
%S 13,46,229,1608,7335,20304,92391,635710,2892133,8001886,36403981,
%T 250470288,1139495223,3152724936,14343078279,98684659918,448958227885,
%U 1242165625054,5651136440101,38881505539560,176888402293623,489410103548496
%N Numbers n such that T(n) + T(n+1) + ... + T(n+10) is a square, where T(m) = A000217(m) is the m-th triangular number.
%C Positive integers n such that 11*n^2 + 121*n + 440 = 2*m^2 for some integer m. - _Max Alekseyev_, Jan 20 2010
%H Vincenzo Librandi, <a href="/A116476/b116476.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,394,-394,0,0,-1,1).
%F For n>8, a(n) = 394*a(n-4) - a(n-8) + 2156. - _Max Alekseyev_, Jan 20 2010
%F G.f.: x*(2*x^8+7*x^7+15*x^6+33*x^5-605*x^4-1379*x^3-183*x^2-33*x-13)/((x-1)*(x^8-394*x^4+1)). - _Colin Barker_, Nov 22 2012
%e 13 belongs to this sequence since T(13) + T(14) + ... + T(23) = 91 + 105 + 120 + 136 + 153 + 171 + 190 + 210 + 231 + 253 + 276 = 1936 = 44^2.
%t For[n = 1, n < 100000, n++, If[IntegerQ[Sqrt[Sum[i*(i+1)/2, {i, n, n + 10}]]], Print[n]]] (* _Stefan Steinerberger_, Mar 30 2006 *)
%t LinearRecurrence[{1,0,0,394,-394,0,0,-1,1},{13,46,229,1608,7335,20304,92391,635710,2892133},30] (* _Harvey P. Dale_, Sep 01 2017 *)
%Y Cf. A176541, A176542, A165517, A202391
%K nonn,easy
%O 1,1
%A Edward Fedorovich (chipramy(AT)012.net.il), Mar 29 2006
%E Extended by _Max Alekseyev_, Jan 20 2010