This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A259415 #16 Mar 19 2023 17:46:07
%S A259415 1326,9180,24531,1979055,5325216,39529386,106368405,8616365901,
%T A259415 23185550130,172110498456,463127571831,37515654714891,100949879501796,
%U A259415 749369070309030,2016457340944761,163343152011830505,439535752164830646,3262752760014579156
%N A259415 Triangular numbers (A000217) that are the sum of seventeen consecutive triangular numbers.
%H A259415 Colin Barker, <a href="/A259415/b259415.txt">Table of n, a(n) for n = 1..1000</a>
%H A259415 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,4354,-4354,0,0,-1,1).
%F A259415 G.f.: -51*x*(11*x^8 +15*x^6 +154*x^5 -47593*x^4 +38324*x^3 +301*x^2 +154*x +26) / ((x -1)*(x^2 -8*x -1)*(x^2 +8*x -1)*(x^4 +66*x^2 +1)).
%e A259415 1326 is in the sequence because T(51) = 1326 = 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 + 91 + 105 + 120 + 136 + 153 + 171 + 190 = T(3) + ... + T(19).
%t A259415 LinearRecurrence[{1, 0, 0, 4354, -4354, 0, 0, -1, 1}, {1326, 9180, 24531, 1979055, 5325216, 39529386, 106368405, 8616365901, 23185550130}, 30] (* _Vincenzo Librandi_, Jun 27 2015 *)
%t A259415 Module[{nn=10^6},Select[Total/@Partition[Accumulate[Range[nn]],17,1],OddQ[ Sqrt[8#+1]]&]] (* _Harvey P. Dale_, Mar 19 2023 *)
%o A259415 (PARI) Vec(-51*x*(11*x^8 +15*x^6 +154*x^5 -47593*x^4 +38324*x^3 +301*x^2 +154*x +26) / ((x -1)*(x^2 -8*x -1)*(x^2 +8*x -1)*(x^4 +66*x^2 +1)) + O(x^30))
%Y A259415 Cf. A000217, A001110, A129803, A131557, A257711, A257712, A257713, A259413, A259414.
%K A259415 nonn,easy
%O A259415 1,1
%A A259415 _Colin Barker_, Jun 26 2015