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 A274603 #21 Jul 08 2016 11:13:15 %S A274603 45,4455,436590,42781410,4192141635,410787098865,40252943547180, %T A274603 3944377680524820,386508759747885225,37873914077612227275, %U A274603 3711257070846250387770,363665319028854925774230,35635490007756936475486815,3491914355441150919671933685 %N A274603 Numbers n such that 2*n+1 and 3*n+1 are both triangular numbers. %C A274603 Inspired by A274579. %C A274603 a(n+1) / a(n) goes to 49 + 20*sqrt(6) when n goes to infinity. %C A274603 Intersection of A045943 and A074377. - _Colin Barker_, Jun 30 2016 %H A274603 Colin Barker, <a href="/A274603/b274603.txt">Table of n, a(n) for n = 1..500</a> %H A274603 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (99,-99,1). %F A274603 From _Colin Barker_, Jun 30 2016: (Start) %F A274603 a(n) = 99*a(n-1)-99*a(n-2)+a(n-3) for n>3. %F A274603 G.f.: 45*x / ((1-x)*(1-98*x+x^2)). %F A274603 (End) %e A274603 45 is a term because 2*45 + 1 = 91 and 3*45 + 1 = 136 are both triangular numbers. %o A274603 (PARI) isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(3*n+1, 3); %o A274603 (PARI) Vec(45*x/((1-x)*(1-98*x+x^2)) + O(x^20)) \\ _Colin Barker_, Jun 30 2016 %Y A274603 Cf. A000217, A045943, A074377, A274579. %K A274603 nonn,easy %O A274603 1,1 %A A274603 _Altug Alkan_, Jun 30 2016 %E A274603 More terms from _Colin Barker_, Jun 30 2016