%I A056123
%S A056123 1,11,32,85,223,584,1529,4003,10480,27437,71831,188056,492337,1288955,
%T A056123 3374528,8834629,23129359,60553448,158530985,415039507,1086587536,
%U A056123 2844723101,7447581767,19498022200,51046484833,133641432299
%N A056123 a(n)=3a(n-1)-a(n-2); a(0)=1, a(1)=11.
%H A056123 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A056123 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A056123 a(n)={11*[((3+sqrt(5))/2)^n - ((3-sqrt(5))/2)^n]-[((3+sqrt(5))/2)^(n-1) 
               - ((3-sqrt(5))/2)^(n-1)]}/sqrt(5).
%F A056123 G.f.(x)=(1+8x)/(1-3x+x^2).
%F A056123 6*Lucas(2n+1) - Fibonacci(2n+5).
%Y A056123 Cf. A055850.
%Y A056123 Sequence in context: A059134 A007790 A048773 this_sequence A006655 A018956 
               A018947
%Y A056123 Adjacent sequences: A056120 A056121 A056122 this_sequence A056124 A056125 
               A056126
%K A056123 easy,nonn
%O A056123 0,2
%A A056123 Barry E. Williams, Jul 06 2000