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 A251730 #11 Jun 08 2016 11:05:17
%S A251730 10,152,2130,29680,413402,5757960,80198050,1117014752,15558008490,
%T A251730 216695104120,3018173449202,42037733184720,585510091136890,
%U A251730 8155103542731752,113585939507107650,1582048049556775360,22035086754287747402,306909166510471688280
%N A251730 Numbers n such that the sum of the triangular numbers T(n) and T(n+1) is equal to the sum of two pentagonal numbers P(m) and P(m+1) for some m.
%C A251730 Also nonnegative integers y in the solutions to 3*x^2-y^2+2*x-2*y = 0, the corresponding values of x being A122770.
%H A251730 Colin Barker, <a href="/A251730/b251730.txt">Table of n, a(n) for n = 1..874</a>
%H A251730 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (15,-15,1).
%F A251730 a(n) = 15*a(n-1)-15*a(n-2)+a(n-3).
%F A251730 G.f.: -2*x*(x+5) / ((x-1)*(x^2-14*x+1)).
%F A251730 a(n) = (-6-(7-4*sqrt(3))^n*(-3+sqrt(3))+(3+sqrt(3))*(7+4*sqrt(3))^n)/6. - _Colin Barker_, Mar 05 2016
%e A251730 10 is in the sequence because T(10)+T(11) = 55+56 = 121 = 51+70 = P(6)+P(7).
%t A251730 LinearRecurrence[{15,-15,1},{10,152,2130},30] (* _Harvey P. Dale_, Jun 08 2016 *)
%o A251730 (PARI) Vec(-2*x*(x+5)/((x-1)*(x^2-14*x+1)) + O(x^100))
%Y A251730 Cf. A000217, A000326, A122770.
%K A251730 nonn,easy
%O A251730 1,1
%A A251730 _Colin Barker_, Dec 07 2014