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 A249164 #14 Jun 13 2015 00:55:17 %S A249164 1,3,113,331,11121,32483,1089793,3183051,106788641,311906563, %T A249164 10464197073,30563660171,1025384524561,2994926790243,100477219209953, %U A249164 293472261783691,9845742098050881,28757286728011523,964782248389776433,2817920627083345611,94538814600100039601 %N A249164 Numbers n such that the triangular number T(n) is equal to the sum of the pentagonal numbers P(m) and P(m+1) for some m. %C A249164 Also nonnegative integers y in the solutions to 6*x^2-y^2+4*x-y+2 = 0, the corresponding values of x being A122513. %H A249164 Colin Barker, <a href="/A249164/b249164.txt">Table of n, a(n) for n = 1..1000</a> %H A249164 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,98,-98,-1,1). %F A249164 a(n) = a(n-1)+98*a(n-2)-98*a(n-3)-a(n-4)+a(n-5). %F A249164 G.f.: -x*(x+1)^2*(11*x^2+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)). %e A249164 113 is in the sequence because T(113) = 6441 = 3151+3290 = P(46)+P(47). %o A249164 (PARI) Vec(-x*(x+1)^2*(11*x^2+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100)) %Y A249164 Cf. A000217, A000326, A122513. %K A249164 nonn,easy %O A249164 1,2 %A A249164 _Colin Barker_, Dec 15 2014