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%I #14 Aug 16 2015 12:04:01
%S 2080,414505,28815436,49317346,3428789455,698283666730,48548229019381,
%T 83089887991201,5776831256176630,1176469718198438755,
%U 81794153348207147926,139990009467226925656,9732816854065394603605,1982118534159467652450580,137806953149317550935817071
%N Triangular numbers (A000217) that are the sum of thirteen consecutive triangular numbers.
%H Colin Barker, <a href="/A259414/b259414.txt">Table of n, a(n) for n = 1..641</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1684802,-1684802,0,0,-1,1).
%F G.f.: -13*x*(7*x^8 +153*x^6 +31725*x^5 -9608927*x^4 +1577070*x^3 +2184687*x^2 +31725*x +160) / ((x -1)*(x^2 -36*x -1)*(x^2 +36*x -1)*(x^4 +1298*x^2 +1)).
%e 2080 is in the sequence because T(64) = 2080 = 66 + 78 + 91 + 105 + 120 + 136 + 153 + 171 + 190 + 210 + 231 + 253 + 276 = T(11) + ... + T(23).
%t LinearRecurrence[{1, 0, 0, 1684802, -1684802, 0, 0, -1, 1}, {2080, 414505, 28815436, 49317346, 3428789455, 698283666730, 48548229019381, 83089887991201, 5776831256176630}, 30] (* _Vincenzo Librandi_, Jun 27 2015 *)
%o (PARI) Vec(-13*x*(7*x^8 +153*x^6 +31725*x^5 -9608927*x^4 +1577070*x^3 +2184687*x^2 +31725*x +160) / ((x -1)*(x^2 -36*x -1)*(x^2 +36*x -1)*(x^4 +1298*x^2 +1)) + O(x^20))
%Y Cf. A000217, A001110, A129803, A131557, A257711, A257712, A257713, A259413, A259415.
%K nonn,easy
%O 1,1
%A _Colin Barker_, Jun 26 2015
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