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 A251914 #17 Mar 03 2016 06:05:41
%S A251914 0,98,9700,950598,93149000,9127651498,894416697900,87643708742798,
%T A251914 8588189040096400,841554882220704498,82463790268588944500,
%U A251914 8080609891439495856598,791817305570802005002200,77590015336047156994359098,7603029685627050583442189500
%N A251914 Numbers n such that the sum of the triangular numbers T(n) and T(n+1) is equal to the pentagonal number P(m) for some m.
%C A251914 Also nonnegative integers x in the solutions to 2*x^2-3*y^2+4*x+y+2 = 0, the corresponding values of y being A046172.
%H A251914 Colin Barker, <a href="/A251914/b251914.txt">Table of n, a(n) for n = 1..503</a>
%H A251914 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (99,-99,1).
%F A251914 a(n) = A046173(n)-1.
%F A251914 a(n) = 99*a(n-1)-99*a(n-2)+a(n-3).
%F A251914 G.f.: 2*x^2*(x-49) / ((x-1)*(x^2-98*x+1)).
%F A251914 a(n) = 2*(-1/2+1/48*(49+20*sqrt(6))^(-n)*(-12-5*sqrt(6)+(-12+5*sqrt(6))*(49+20*sqrt(6))^(2*n))). - _Colin Barker_, Mar 03 2016
%e A251914 98 is in the sequence because T(98)+T(99) = 4851+4950 = 9801 = P(81).
%t A251914 LinearRecurrence[{99, -99, 1}, {0, 98, 9700}, 20] (* _Vincenzo Librandi_, Mar 03 2016 *)
%o A251914 (PARI) concat(0, Vec(2*x^2*(x-49) / ((x-1)*(x^2-98*x+1)) + O(x^100)))
%Y A251914 Cf. A000217, A000326, A046172.
%K A251914 nonn,easy
%O A251914 1,2
%A A251914 _Colin Barker_, Dec 11 2014