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RMS values associated with A084231.
6

%I #37 Nov 10 2021 15:38:41

%S 1,195,37829,7338631,1423656585,276182038859,53577891882061,

%T 10393834843080975,2016350381665827089,391161580208327374291,

%U 75883330210033844785365,14720974899166357560986519,2855793247108063332986599321,554009168964065120241839281755

%N RMS values associated with A084231.

%H Indranil Ghosh, <a href="/A084232/b084232.txt">Table of n, a(n) for n = 0..436</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (194,-1).

%F 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 a(n) = floor(((7*sqrt(3) + 12)/24)*(56*sqrt(3) + 97)^n).

%F a(n+2) = 194*a(n+1) - a(n).

%F G.f.: (1-x)/(1-194*x+x^2). - _Philippe Deléham_, Nov 18 2008

%F a(n)^2 = (Sum_{i=1..A084231(n+1)}i^2)/A084231(n+1). - _Bruno Berselli_, Oct 17 2012

%e a(1)=195 because 195 = sqrt((Sum_{k=1..337}k^2)/337) and 337 = A084231(1).

%t LinearRecurrence[{194,-1},{1,195},20] (* _Harvey P. Dale_, Nov 10 2021 *)

%Y Cf. A084231, A217855.

%K nonn,easy

%O 0,2

%A _Ignacio Larrosa Cañestro_, May 20 2003