Search: id:A106729
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%I A106729
%S A106729 5,10,25,65,170,445,1165,3050,7985,20905,54730,143285,375125,982090,
%T A106729 2571145,6731345,17622890,46137325,120789085,316229930
%N A106729 Sum of two consecutive squares of Lucas numbers (A001254).
%H A106729 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A106729 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A106729 a(n) = L(n)^2 + L(n+1)^2 = 5*{F(n)^2 + F(n+1)^2} = 5*A001519(n).
%F A106729 a(n)=3a(n-1)-a(n-2) - T. D. Noe (noe(AT)sspectra.com), Dec 11 2006
%F A106729 G.f.: 5(1-x)/(1-3x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 16 2008]
%F A106729 a(n)=(5/2)*[(3/2)+(1/2)*sqrt(5)]^n+(1/2)*[(3/2)+(1/2)*sqrt(5)]^n*sqrt(5)-(1/
               2)*[(3/2)-(1/2)*sqrt(5)]^n *sqrt(5)+(5/2)*[(3/2)-(1/2)*sqrt(5)]^n, 
               with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 19 2008]
%Y A106729 Cf. A000204.
%Y A106729 Sequence in context: A045620 A025625 A112024 this_sequence A038252 A083010 
               A166388
%Y A106729 Adjacent sequences: A106726 A106727 A106728 this_sequence A106730 A106731 
               A106732
%K A106729 nonn
%O A106729 0,1
%A A106729 Lekraj Beedassy (blekraj(AT)yahoo.com), May 14 2005
%E A106729 Corrected by T. D. Noe (noe(AT)sspectra.com), Dec 11 2006

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