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%I #15 Jun 27 2015 06:26:23
%S 1485,7260,28920,142845,2112540,10440165,41673885,205953660,
%T 3046252485,15054681960,60093684540,296985006165,4392693942120,
%U 21708840917445,86655051404085,428252172907560,6334261618255845,31304133548245020,124956524030977320,617539336347666645
%N Triangular numbers (A000217) that are the sum of ten consecutive triangular numbers.
%H Colin Barker, <a href="/A257713/b257713.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 (1,0,0,1442,-1442,0,0,-1,1).
%F G.f.: -15*x*(8*x^8-5*x^7+5*x^5-11445*x^4+7595*x^3+1444*x^2+385*x+99) / ((x-1)*(x^2-6*x-1)*(x^2+6*x-1)*(x^4+38*x^2+1)).
%e 1485 is in the sequence because T(54) = 1485 = 78+91+105+120+136+153+171+190+210+231 = T(12)+ ... +T(21).
%t LinearRecurrence[{1, 0, 0, 1442, -1442, 0, 0, -1, 1}, {1485, 7260, 28920, 142845, 2112540, 10440165, 41673885, 205953660, 3046252485}, 30] (* _Vincenzo Librandi_, Jun 27 2015 *)
%o (PARI) Vec(-15*x*(8*x^8-5*x^7+5*x^5-11445*x^4+7595*x^3+1444*x^2+385*x+99) / ((x-1)*(x^2-6*x-1)*(x^2+6*x-1)*(x^4+38*x^2+1)) + O(x^100))
%Y Cf. A000217, A001110, A129803, A131557, A257711, A257712, A259413, A259414, A259415.
%K nonn
%O 1,1
%A _Colin Barker_, May 05 2015
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