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%I #18 Jan 01 2024 11:32:06
%S 1,5,39,307,2417,19029,149815,1179491,9286113,73109413,575589191,
%T 4531604115,35677243729,280886345717,2211413522007,17410421830339,
%U 137071961120705,1079165267135301,8496250175961703,66890836140558323
%N a(0)=1, a(1)=5, a(n)=8*a(n-1)-a(n-2).
%C 15*a(n)^2-14 is a square for all n.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-1).
%H <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%F 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.
%t LinearRecurrence[{8,-1},{1,5},20] (* _Harvey P. Dale_, Feb 25 2016 *)
%o (PARI) a(n)=subst(19*poltchebi(n)-poltchebi(n-1),x,4)/15
%Y Cf. a(n) = A001090(n+1) - 3*A001090(n).
%K nonn,easy
%O 0,2
%A _Michael Somos_, Apr 10 2005
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