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 A259157 #14 Aug 04 2025 11:28:42
%S A259157 3,3570,4119885,4754343828,5486508657735,6331426236682470,
%T A259157 7306460390622912753,8431648959352604634600,9730115592632515125415755,
%U A259157 11228544962248963102125146778,12957731156319710787337293966165,14953210525847983999624135111807740
%N A259157 Positive triangular numbers (A000217) that are hexagonal numbers (A000384) divided by 2.
%C A259157 Intersection of A000217 and A033991 (even hexagonal numbers divided by 2). - _Michel Marcus_, Jun 20 2015
%H A259157 Colin Barker, <a href="/A259157/b259157.txt">Table of n, a(n) for n = 1..327</a>
%H A259157 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1155,-1155,1).
%F A259157 G.f.: -3*x*(35*x+1) / ((x-1)*(x^2-1154*x+1)).
%F A259157 a(n) = 1155*a(n-1) - 1155*a(n-2) + a(n-3). - _Wesley Ivan Hurt_, Aug 04 2025
%e A259157 3 is in the sequence because 3 is the 2nd triangular number, and 2*3 is the 2nd hexagonal number.
%t A259157 LinearRecurrence[{1155, -1155, 1}, {3, 3570, 4119885}, 20] (* _Vincenzo Librandi_, Jun 20 2015 *)
%o A259157 (PARI) Vec(-3*x*(35*x+1)/((x-1)*(x^2-1154*x+1)) + O(x^20))
%Y A259157 Cf. A000217, A000384, A033991, A259156, A259158-A259167.
%K A259157 nonn,easy
%O A259157 1,1
%A A259157 _Colin Barker_, Jun 19 2015