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 A077290 #38 May 12 2022 17:48:40
%S A077290 0,6,36,630,3570,61776,349866,6053460,34283340,593177346,3359417496,
%T A077290 58125326490,329188631310,5695688818716,32257126450926,
%U A077290 558119378907720,3160869203559480,54690003444137886,309732924822378156,5359062218146605150,30350665763389499850
%N A077290 Triangular numbers that are 6 times other triangular numbers.
%H A077290 Colin Barker, <a href="/A077290/b077290.txt">Table of n, a(n) for n = 0..1000</a>
%H A077290 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 A077290 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 A077290 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 A077290 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,98,-98,-1,1).
%F A077290 a(n) = 6*A077289(n).
%F A077290 G.f.: -6*x*(x^2+5*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)). - _Colin Barker_, Jul 02 2013
%F A077290 a(n) = 98*a(n-2) - a(n-1) + 42. - _Vladimir Pletser_, Feb 20 2021
%e A077290 The k-th triangular number is T(k) = k*(k+1)/2, so T(35)/T(14) = (35*36/2)/(14*15/2) = 630/105 = 6, so T(35)=630 is a term. - _Jon E. Schoenfield_, Feb 20 2021
%p A077290 f := gfun:-rectoproc({a(-2) = 6, a(-1) = 0, a(0) = 0, a(1) = 6, a(n) = 98*a(n-2)-a(n-4)+42}, a(n), remember); map(f, [`$`(0 .. 1000)])[]; # _Vladimir Pletser_, Feb 20 2021
%t A077290 CoefficientList[Series[-6 x (x^2 + 5 x + 1)/((x - 1) (x^2 - 10 x + 1) (x^2 + 10 x + 1)), {x, 0, 20}], x] (* _Michael De Vlieger_, Apr 21 2021 *)
%o A077290 (PARI)
%o A077290 T(n)=n*(n+1)\2;
%o A077290 istriang(n)=issquare(8*n+1);
%o A077290 for(n=0,10^10, t=T(n); if ( t%6==0 && istriang(t\6), print1(t,", ") ) );
%o A077290 \\ _Joerg Arndt_, Jul 03 2013
%o A077290 (PARI) concat(0, Vec(-6*x*(x^2+5*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))) \\ _Colin Barker_, May 15 2015
%Y A077290 Cf. A077288, A077289, A077291.
%Y A077290 Subsequence of A000217.
%K A077290 easy,nonn
%O A077290 0,2
%A A077290 Bruce Corrigan (scentman(AT)myfamily.com), Nov 03 2002
%E A077290 More terms from _Joerg Arndt_, Jul 03 2013