cp's OEIS Frontend

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.

A257713 Triangular numbers (A000217) that are the sum of ten consecutive triangular numbers.

This page as a plain text file.
%I A257713 #15 Jun 27 2015 06:26:23
%S A257713 1485,7260,28920,142845,2112540,10440165,41673885,205953660,
%T A257713 3046252485,15054681960,60093684540,296985006165,4392693942120,
%U A257713 21708840917445,86655051404085,428252172907560,6334261618255845,31304133548245020,124956524030977320,617539336347666645
%N A257713 Triangular numbers (A000217) that are the sum of ten consecutive triangular numbers.
%H A257713 Colin Barker, <a href="/A257713/b257713.txt">Table of n, a(n) for n = 1..1000</a>
%H A257713 <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 A257713 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 A257713 1485 is in the sequence because T(54) = 1485 = 78+91+105+120+136+153+171+190+210+231 = T(12)+ ... +T(21).
%t A257713  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 A257713 (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 A257713 Cf. A000217, A001110, A129803, A131557, A257711, A257712, A259413, A259414, A259415.
%K A257713 nonn
%O A257713 1,1
%A A257713 _Colin Barker_, May 05 2015