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%I #5 Sep 29 2016 16:41:04
%S 625,18769,635209,21576025,732947329,24898630849,845820499225,
%T 28732998340489,976076123075089,33157855186210225,1126391000208070249,
%U 38264136151888175929,1299854238163989909025,44156779961423768728609
%N a(n) = 34*a(n-1)-a(n-2)-2312 for n > 2; a(1)=625, a(2)=18769.
%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+(387-182*sqrt(2))*(17+12*sqrt(2))^n+(387+182*sqrt(2))*(17-12*sqrt(2))^n)/8.
%F G.f.: x*(625-3106*x+169*x^2)/((1-x)*(1-34*x+x^2)).
%e a(3) = 34*a(2)-a(1)-2312 = 34*18769-625-2312 = 635209.
%t RecurrenceTable[{a[1]==625,a[2]==18769,a[n]==34a[n-1]-a[n-2]-2312},a,{n,20}] (* or *) LinearRecurrence[{35,-35,1},{625,18769,635209},20] (* _Harvey P. Dale_, Sep 29 2016 *)
%o (PARI) {m=14; v=concat([625 ,18769], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-2312); v}
%Y Third 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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