Search: id:A002310
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%I A002310
%S A002310 1,2,9,43,206,987,4729,22658,108561,520147,2492174,11940723,
%T A002310 57211441,274116482,1313370969,6292738363,30150320846,144458865867,
%U A002310 692144008489,3316261176578,15889161874401,76129548195427
%N A002310 a(n) = 5*a(n-1) - a(n-2).
%C A002310 Together with A002320 these are the two sequences satisfying ( a(n)^2+a(n-1)^2 
               )/(1 - a(n)a(n-1)) is an integer, in both cases this integer is -5. 
               - Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 26 2001
%D A002310 From a posting to Netnews group sci.math by ksbrown(AT)seanet.com (K. 
               S. Brown) on Aug 15 1996.
%H A002310 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A002310 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A002310 MathPages, <a href="http://www.mathpages.com/home/kmath334.htm">N = (x^2 
               + y^2)/(1+xy) is a Square</a>
%F A002310 Sequences A002310, A002320 and A049685 have this in common: each one 
               satisfies a(n+1) = (a(n)^2+5)/a(n-1) - Graeme McRae (g_m(AT)mcraefamily.com), 
               Jan 30 2005
%F A002310 G.f.: (1-3x)/(1-5x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 16 2008]
%F A002310 a(n)=(1/42)*sqrt(21)*[(5/2)-(1/2)*sqrt(21)]^n-1/42*(5/2+1/2*sqrt(21))^n*sqrt(21)+(1/
               2)*[(5/2)+(1 /2)*sqrt(21)]^n+(1/2)*[(5/2)-(1/2)*sqrt(21)]^n, with 
               n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 21 2008]
%Y A002310 Sequence in context: A132847 A121365 A018960 this_sequence A055728 A006795 
               A055824
%Y A002310 Adjacent sequences: A002307 A002308 A002309 this_sequence A002311 A002312 
               A002313
%K A002310 nonn
%O A002310 0,2
%A A002310 Joe Keane (jgk(AT)jgk.org)

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