%I A097512
%S A097512 11,15,34,87,227,594,1555,4071,10658,27903,73051,191250,500699,1310847,
%T A097512 3431842,8984679,23522195,61581906,161223523,422088663,1105042466,
%U A097512 2893038735,7574073739,19829182482,51913473707,135911238639
%N A097512 6*Lucas(2n) - Fib(2n+2).
%C A097512 Sequence relates bisections of Lucas and Fibonacci numbers.
%H A097512 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A097512 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A097512 a(n) = 8*Lucas(2n) - Lucas(2n+2) - 2*Fib(2n-1) = 8*A005248(n) - A005248(n+1) 
               - 2*A001519(n).
%F A097512 a(n+1)/a(n) approaches the golden ratio phi + 1 = (3+sqrt(5))/2.
%F A097512 a(n)=3*a(n-1)-a(n-2) with a(0)=11 and a(1)=15. G.f.: (11-18x)/(1-3x+x^2). 
               [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 16 2008]
%F A097512 a(n)=(11/2)*[(3/2)+(1/2)*sqrt(5)]^n-(3/10)*[(3/2)+(1/2)*sqrt(5)]^n*sqrt(5)+(3/
               10)*[(3/2)-(1/2) *sqrt(5)]^n*sqrt(5)+(11/2)*[(3/2)-(1/2)*sqrt(5)]^n, 
               with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 19 2008]
%Y A097512 Cf. A005248, A005248, A022133.
%Y A097512 Sequence in context: A009433 A030099 A085597 this_sequence A032490 A068483 
               A115779
%Y A097512 Adjacent sequences: A097509 A097510 A097511 this_sequence A097513 A097514 
               A097515
%K A097512 nonn
%O A097512 0,1
%A A097512 Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 26 2004
%E A097512 New definition from Ralf Stephan, Dec 01, 2004
%E A097512 More terms from Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 19 2009