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 A251924 #14 Feb 04 2019 12:29:55
%S A251924 0,34,1188,40390,1372104,46611178,1583407980,53789260174,
%T A251924 1827251437968,62072759630770,2108646576008244,71631910824649558,
%U A251924 2433376321462076760,82663163018885960314,2808114166320660573948,95393218491883573553950,3240561314557720840260384
%N A251924 Numbers n such that the sum of the triangular numbers T(n) and T(n+1) is equal to a hexagonal number H(m) for some m.
%C A251924 Also nonnegative integers x in the solutions to 2*x^2-4*y^2+4*x+2*y+2 = 0, the corresponding values of y being A008844.
%C A251924 First bisection of A076708. [_Bruno Berselli_, Dec 11 2014]
%H A251924 Colin Barker, <a href="/A251924/b251924.txt">Table of n, a(n) for n = 1..653</a>
%H A251924 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (35,-35,1).
%F A251924 a(n) = 35*a(n-1)-35*a(n-2)+a(n-3).
%F A251924 G.f.: 2*x^2*(x-17) / ((x-1)*(x^2-34*x+1)).
%F A251924 a(n) = (-8-(4+3*sqrt(2))*(17+12*sqrt(2))^(-n)+(-4+3*sqrt(2))*(17+12*sqrt(2))^n)/8. - _Colin Barker_, Mar 02 2016
%e A251924 34 is in the sequence because T(34)+T(35) = 595+630 = 1225 = H(25).
%t A251924 LinearRecurrence[{35,-35,1},{0,34,1188},20] (* _Harvey P. Dale_, Feb 04 2019 *)
%o A251924 (PARI) concat(0, Vec(2*x^2*(x-17)/((x-1)*(x^2-34*x+1)) + O(x^100)))
%Y A251924 Cf. A000217, A000384, A008844, A076708.
%K A251924 nonn,easy
%O A251924 1,2
%A A251924 _Colin Barker_, Dec 11 2014