%I A105426
%S A105426 1,5,39,307,2417,19029,149815,1179491,9286113,73109413,575589191,
%T A105426 4531604115,35677243729,280886345717,2211413522007,17410421830339,
%U A105426 137071961120705,1079165267135301,8496250175961703,66890836140558323
%N A105426 a(0)=1, a(1)=5, a(n)=8*a(n-1)-a(n-2).
%C A105426 15*a(n)^2-14 is a square for all n.
%H A105426 <a href="Sindx_Tu.html#2wis">Index entries for two-way infinite sequences</
               a>
%H A105426 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A105426 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A105426 G.f.: (1-3x)/(1-8x+x^2). a(n)=2*A105045(2*n+1)-1. a(-n)=2*A105045(2*n)-1, 
               if n>0.
%F A105426 a(n)=(1/2)*[4-sqrt(15)]^n-(1/30)*[4-sqrt(15)]^n*sqrt(15)+(1/2)*[4+sqrt(15)]^n+(1/
               30)*sqrt(15) *[4+sqrt(15)]^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), 
               Jul 08 2008
%o A105426 (PARI) a(n)=subst(19*poltchebi(n)-poltchebi(n-1),x,4)/15
%Y A105426 Cf. a(n) = A001090(n+1) - 3*A001090(n).
%Y A105426 Sequence in context: A053573 A003482 A135849 this_sequence A115187 A129763 
               A070767
%Y A105426 Adjacent sequences: A105423 A105424 A105425 this_sequence A105427 A105428 
               A105429
%K A105426 nonn
%O A105426 0,2
%A A105426 Michael Somos, Apr 10 2005