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%I #6 Jun 13 2015 00:53:00
%S 169,2809,93025,3157729,107267449,3643933225,123786459889,
%T 4205095700689,142849467361225,4852676794578649,164848161548310529,
%U 5599984815847977025,190234635577282906009,6462377624811770824969
%N a(n) = 34*a(n-1)-a(n-2)-2312 for n > 2; a(1)=169, a(2)=2809.
%C lim_{n -> infinity} a(n)/a(n-1) = (17+12*sqrt(2)).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (35, -35, 1).
%F a(n) = (578+ (2211-1550*sqrt(2))*(17+12*sqrt(2))^n+(2211+1550*sqrt(2))*(17-12*sqrt(2))^n)/8.
%F G.f.: x*(169-3106*x+625*x^2)/((1-x)*(1-34*x+x^2)).
%e a(3) = 34*a(2)-a(1)-2312 = 34*2809-169-2312 = 93025.
%t LinearRecurrence[{35,-35,1},{169,2809,93025},20] (* _Harvey P. Dale_, Nov 15 2014 *)
%o (PARI) {m=14; v=concat([169, 2809], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-2312); v}
%Y First trisection of A156159.
%Y Cf. A156164 (decimal expansion of (17+12*sqrt(2))).
%K nonn
%O 1,1
%A _Klaus Brockhaus_, Feb 09 2009
%E G.f. corrected by _Klaus Brockhaus_, Sep 23 2009
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