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 A084232 #42 Aug 24 2025 19:43:50
%S A084232 1,195,37829,7338631,1423656585,276182038859,53577891882061,
%T A084232 10393834843080975,2016350381665827089,391161580208327374291,
%U A084232 75883330210033844785365,14720974899166357560986519,2855793247108063332986599321,554009168964065120241839281755
%N A084232 RMS values associated with A084231.
%C A084232 From _Klaus Purath_, Aug 20 2025: (Start)
%C A084232 Solutions to the Pell equation (7*b(n))^2 - 3*(4*a(n))^2 = 1. The corresponding b(n) are given by A302332.
%C A084232 For any two consecutive terms (x,y), x^2 - 194*x*y + y^2 - 196 = 0. By analogy to this, for three consecutive terms (x, y, z), y^2 - x*z - 196 = 0. (End)
%H A084232 Indranil Ghosh, <a href="/A084232/b084232.txt">Table of n, a(n) for n = 0..436</a>
%H A084232 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A084232 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (194,-1).
%F A084232 a(n) = ((7+4*sqrt(3))^(2*n+1)-(7-4*sqrt(3))^(2*n+1))/(8*sqrt(3)). [simplified by _Bruno Berselli_, Oct 19 2012]
%F A084232 a(n) = floor(((7*sqrt(3) + 12)/24)*(56*sqrt(3) + 97)^n).
%F A084232 a(n+2) = 194*a(n+1) - a(n).
%F A084232 G.f.: (1-x)/(1-194*x+x^2). - _Philippe Deléham_, Nov 18 2008
%F A084232 a(n)^2 = (Sum_{i=1..A084231(n+1)}i^2)/A084231(n+1). - _Bruno Berselli_, Oct 17 2012
%e A084232 a(1)=195 because 195 = sqrt((Sum_{k=1..337}k^2)/337) and 337 = A084231(1).
%t A084232 LinearRecurrence[{194,-1},{1,195},20] (* _Harvey P. Dale_, Nov 10 2021 *)
%Y A084232 Cf. A084231, A217855, A302332.
%K A084232 nonn,easy,changed
%O A084232 0,2
%A A084232 _Ignacio Larrosa Cañestro_, May 20 2003