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%I #13 Aug 16 2015 12:04:01
%S 2145,3916,7381,13530,843051,1547920,2926990,5374281,335521560,
%T 616057651,1164924046,2138939715,133536727236,245189386585,
%U 463636832725,851292621696,53147281907775,97584759792586,184526294489911,338812324484700,21152484662556621
%N Triangular numbers (A000217) that are the sum of eleven consecutive triangular numbers.
%H Colin Barker, <a href="/A259413/b259413.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 (1,0,0,398,-398,0,0,-1,1).
%F G.f.: -11*x*(6*x^8-x^7+x^5-2199*x^4+559*x^3+315*x^2+161*x+195) / ((x-1)*(x^4-20*x^2+1)*(x^4+20*x^2+1)).
%e 2145 is in the sequence because T(65) = 2145 = 105 + 120 + 136 + 153 + 171 + 190 + 210 + 231 + 253 + 276 + 300 = T(14) + ... + T(24).
%t LinearRecurrence[{1, 0, 0, 398, -398, 0, 0, -1, 1}, {2145, 3916, 7381, 13530, 843051, 1547920, 2926990, 5374281, 335521560}, 30] (* _Vincenzo Librandi_, Jun 27 2015 *)
%o (PARI) Vec(-11*x*(6*x^8-x^7+x^5-2199*x^4+559*x^3+315*x^2+161*x+195)/((x-1)*(x^4-20*x^2+1)*(x^4+20*x^2+1)) + O(x^30))
%Y Cf. A000217, A001110, A129803, A131557, A257711, A257712, A257713, A259414, A259415.
%K nonn,easy
%O 1,1
%A _Colin Barker_, Jun 26 2015
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