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 A154147 #21 Dec 23 2024 14:53:42
%S A154147 3,9,30,60,179,353,1046,2060,6099,12009,35550,69996,207203,407969,
%T A154147 1207670,2377820,7038819,13858953,41025246,80775900,239112659,
%U A154147 470796449,1393650710,2744002796,8122791603,15993220329,47343098910,93215319180,275935801859
%N A154147 Indices k such that 19 plus the k-th triangular number is a perfect square.
%H A154147 Colin Barker, <a href="/A154147/b154147.txt">Table of n, a(n) for n = 1..500</a>
%H A154147 F. T. Adams-Watters, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2009-October/002504.html">SeqFan Discussion</a>, Oct 2009
%H A154147 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-6,-1,1).
%F A154147 {k: 19+k*(k+1)/2 in A000290}.
%F A154147 a(n)= +a(n-1) +6*a(n-2) -6*a(n-3) -a(n-4) +a(n-5).
%F A154147 G.f.: x*(3 +6*x +3*x^2 -6*x^3 -4*x^4)/((1-x) * (x^2-2*x-1) * (x^2+2*x-1)).
%e A154147 3*(3+1)/2+19 = 5^2. 9*(9+1)/2+19 = 8^2. 30*(30+1)/2+19 = 22^2. 60*(60+1)/2+19 = 43^2.
%t A154147 Join[{3, 9}, Select[Range[0, 10^5], ( Ceiling[Sqrt[#*(# + 1)/2]] )^2 - #*(# + 1)/2 == 19 &]] (* or *) LinearRecurrence[{1,6,-6,-1,1}, {3,9,30,60,179}, 25] (* _G. C. Greubel_, Sep 03 2016 *)
%o A154147 (PARI) {for (n=0, 10^9, if ( issquare(n*(n+1)\2 + 19), print1(n, ", ") ) ); }
%Y A154147 Cf. A000217, A000290, A006451.
%K A154147 nonn,less
%O A154147 1,1
%A A154147 _R. J. Mathar_, Oct 18 2009