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 A274680 #15 Jul 04 2016 05:53:24
%S A274680 0,16065,545751,21394547226,726784809030,28491418065071115,
%T A274680 967869505172593485,37942420317086720855700,1288925370210688376036076,
%U A274680 50528452330120333959563160501,1716479960463788790499334882595,67289447366315927998308608003134830
%N A274680 Values of n such that 2*n+1 and 4*n+1 are both triangular numbers.
%H A274680 Colin Barker, <a href="/A274680/b274680.txt">Table of n, a(n) for n = 1..325</a>
%H A274680 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1331714,-1331714,-1,1).
%F A274680 Intersection of A074377 and A274681.
%F A274680 G.f.: 459*x^2*(35+1154*x+35*x^2) / ((1-x)*(1-1154*x+x^2)*(1+1154*x+x^2)).
%e A274680 16065 is in the sequence because 2*16065+1 = 32131, 4*16065+1 = 64261, and 32131 and 64261 are both triangular numbers.
%t A274680 Rest@ CoefficientList[Series[459 x^2 (35 + 1154 x + 35 x^2)/((1 - x) (1 - 1154 x + x^2) (1 + 1154 x + x^2)), {x, 0, 12}], x] (* _Michael De Vlieger_, Jul 02 2016 *)
%o A274680 (PARI) isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(4*n+1, 3)
%o A274680 (PARI) concat(0, Vec(459*x^2*(35+1154*x+35*x^2)/((1-x)*(1-1154*x+x^2)*(1+1154*x+x^2)) + O(x^20)))
%Y A274680 Cf. A124174 (2*n+1 and 9*n+1), A274579 (2*n+1 and 5*n+1), A274603 (2*n+1 and 3*n+1).
%K A274680 nonn,easy
%O A274680 1,2
%A A274680 _Colin Barker_, Jul 02 2016