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 A253470 #12 Mar 03 2016 08:45:03 %S A253470 1,5,36,280,2201,17325,136396,1073840,8454321,66560725,524031476, %T A253470 4125691080,32481497161,255726286205,2013328792476,15850904053600, %U A253470 124793903636321,982500325036965,7735208696659396,60899169248238200,479458145289246201,3774765993065731405 %N A253470 Indices of centered triangular numbers (A005448) which are also centered pentagonal numbers (A005891). %C A253470 Also indices of pentagonal numbers (A000326) which are also centered pentagonal numbers (A005891). %C A253470 Also positive integers x in the solutions to 3*x^2 - 5*y^2 - 3*x + 5*y = 0, the corresponding values of y being A182432. %H A253470 Colin Barker, <a href="/A253470/b253470.txt">Table of n, a(n) for n = 1..1000</a> %H A253470 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-9,1). %F A253470 a(n) = 9*a(n-1)-9*a(n-2)+a(n-3). %F A253470 G.f.: x*(4*x-1) / ((x-1)*(x^2-8*x+1)). %F A253470 a(n) = (6-(4-sqrt(15))^n*(3+sqrt(15))+(-3+sqrt(15))*(4+sqrt(15))^n)/12. - _Colin Barker_, Mar 03 2016 %e A253470 5 is in the sequence because the 5th centered triangular number is 31, which is also the 4th centered pentagonal number. %o A253470 (PARI) Vec(x*(4*x-1)/((x-1)*(x^2-8*x+1)) + O(x^100)) %Y A253470 Cf. A005448, A005891, A182432, A253654. %K A253470 nonn,easy %O A253470 1,2 %A A253470 _Colin Barker_, Jan 01 2015