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 A077399 #38 Sep 08 2022 08:45:07
%S A077399 0,3,15,780,3828,198135,972315,50325528,246964200,12782485995,
%T A077399 62727934503,3246701117220,15932648399580,824649301287903,
%U A077399 4046829965558835,209457675826010160,1027878878603544528,53201425010505292755,261077188335334751295,13512952494992518349628
%N A077399 Triangular numbers that are 1/7 of triangular numbers.
%H A077399 Colin Barker, <a href="/A077399/b077399.txt">Table of n, a(n) for n = 0..832</a>
%H A077399 Vladimir Pletser, <a href="https://arxiv.org/abs/2101.00998">Recurrent Relations for Multiple of Triangular Numbers being Triangular Numbers</a>, arXiv:2101.00998 [math.NT], 2021.
%H A077399 Vladimir Pletser, <a href="https://arxiv.org/abs/2102.13494">Triangular Numbers Multiple of Triangular Numbers and Solutions of Pell Equations</a>, arXiv:2102.13494 [math.NT], 2021.
%H A077399 Vladimir Pletser, <a href="https://www.researchgate.net/profile/Vladimir-Pletser/publication/359808848_USING_PELL_EQUATION_SOLUTIONS_TO_FIND_ALL_TRIANGULAR_NUMBERS_MULTIPLE_OF_OTHER_TRIANGULAR_NUMBERS/">Using Pell equation solutions to find all triangular numbers multiple of other triangular numbers</a>, 2022.
%H A077399 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,254,-254,-1,1).
%F A077399 Let b(n) be A077398(n) then a(n) = b(n)*(b(n)+1)/2.
%F A077399 G.f.: -3*x*(x^2+4*x+1) / ((x-1)*(x^2-16*x+1)*(x^2+16*x+1)). - _Colin Barker_, Jul 02 2013
%F A077399 Comment from __Vladimir Pletser_, Feb 21 2021: (Start)
%F A077399 a(n) = 254 a(n - 2) - a (n - 4) + 18.
%F A077399 a(n) = a(n - 1) + 254 (a(n - 2) - a(n - 3)) - (a (n - 4) - a(n - 5)). (End)
%p A077399 f := gfun:-rectoproc({a(-2) = 3, a(-1) = 0, a(0) = 0, a(1) = 3, a(n) = 254*a(n-2)-a(n-4)+18}, a(n), remember); map(f, [`$`(0 .. 1000)])[] #_Vladimir Pletser_, Feb 21 2021
%t A077399 Select[Accumulate[Range[0,5700000]],IntegerQ[(Sqrt[56#+1]-1)/2]&] (* _Harvey P. Dale_, Jan 18 2013 *)
%t A077399 LinearRecurrence[{1,254,-254,-1,1},{0,3,15,780,3828}, 30] (* _G. C. Greubel_, Jan 18 2018 *)
%o A077399 (PARI) concat(0, Vec(-3*x*(x^2+4*x+1)/((x-1)*(x^2-16*x+1)*(x^2+16*x+1)) + O(x^100))) \\ _Colin Barker_, May 15 2015
%o A077399 (Magma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q,30); [0] cat Coefficients(R!(-3*x*(x^2+4*x+1)/((x-1)*(x^2-16*x+1)*(x^2+16*x+1)))); // _G. C. Greubel_, Jan 18 2018
%Y A077399 Cf. A077398, A077400, A077401.
%K A077399 easy,nonn
%O A077399 0,2
%A A077399 Bruce Corrigan (scentman(AT)myfamily.com), Nov 05 2002