%I M4758 #33 Sep 08 2022 08:44:34

%S 10,970,912670090,760223786832147978143718730,

%T 439363892017598816969702791108195858981800447259539613873486126455827777484460810

%N Extracting a square root.

%D Jeffrey Shallit, personal communication.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A006242/b006242.txt">Table of n, a(n) for n = 1..7</a>

%H E. B. Escott, <a href="http://www.jstor.org/stable/2301484">Rapid method for extracting a square root</a>, Amer. Math. Monthly, 44 (1937), 644-646.

%F a(1) = 10, a(n) = a(n-1)^3 - 3*a(n-1) [From Escott]. - _Sean A. Irvine_, Feb 08 2017

%F a(n) = (5 + 2*sqrt(6))^(3^(n-1)) + (5 - 2*sqrt(6))^(3^(n-1)). - _Bruno Berselli_, Feb 10 2017

%F a(n) = 2*T(3^(n-1),5), where T(n,x) deotes the n-th Chebyshev polynomial of the first kind. - _Peter Bala_, Mar 29 2022

%t RecurrenceTable[{a[1]==10, a[n]==a[n-1]^3 - 3 a[n-1]}, a, {n, 8}] (* _Vincenzo Librandi_, Feb 09 2017 *)

%o (Magma) [n eq 1 select 10 else Self(n-1)^3-3*Self(n-1): n in [1..5]]; // _Vincenzo Librandi_, Feb 09 2017

%Y Cf. A006243.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_

%E New offset and a(5) from _Sean A. Irvine_, Feb 08 2017