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%I #41 Dec 30 2023 10:56:22
%S 1,3,14,67,321,1538,7369,35307,169166,810523,3883449,18606722,
%T 89150161,427144083,2046570254,9805707187,46981965681,225104121218,
%U 1078538640409,5167589080827,24759406763726,118629444737803
%N a(n) = 5*a(n-1) - a(n-2).
%C Together with A002310 these are the two sequences satisfying the requirement that (a(n)^2 + a(n-1)^2)/(1 - a(n)*a(n-1)) be an integer; in both cases this integer is -5. - _Floor van Lamoen_, Oct 26 2001
%D From a posting to Netnews group sci.math by ksbrown(AT)seanet.com (K. S. Brown) on Aug 15 1996.
%H Reinhard Zumkeller, <a href="/A002320/b002320.txt">Table of n, a(n) for n = 0..1000</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H MathPages, <a href="http://www.mathpages.com/home/kmath334.htm">N = (x^2 + y^2)/(1+xy) is a Square</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-1).
%F Sequences A002310, A002320 and A049685 have this in common: each one satisfies a(n+1) = (a(n)^2+5)/a(n-1) - _Graeme McRae_, Jan 30 2005
%F G.f.: (1-2x)/(1-5x+x^2). - _Philippe Deléham_, Nov 16 2008
%F a(n) = Sum_{k = 0..n} A238731(n,k)*2^k. - _Philippe Deléham, Mar 05 2014
%t LinearRecurrence[{5,-1},{1,3},30] (* _Harvey P. Dale_, Nov 13 2014 *)
%o (Haskell)
%o a002320 n = a002320_list !! n
%o a002320_list = 1 : 3 :
%o (zipWith (-) (map (* 5) (tail a002320_list)) a002320_list)
%o -- _Reinhard Zumkeller_, Oct 16 2011
%Y Cf. A054477.
%K nonn,easy
%O 0,2
%A Joe Keane (jgk(AT)jgk.org)
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