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%I #5 Jun 30 2023 00:19:49
%S 17,85,493,2873,16745,97597,568837,3315425,19323713,112626853,
%T 656437405,3825997577,22299548057,129971290765,757528196533,
%U 4415197888433,25733659134065,149986756915957,874186882361677,5095134537254105
%N a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 17, a(2) = 85.
%C lim_{n -> infinity} a(n)/a(n-1) = 3+2*sqrt(2).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, -1).
%F a(n) = ((2+sqrt(2))*(3-2*sqrt(2))^n+(2-sqrt(2))*(3+2*sqrt(2))^n)*17/4.
%F G.f.: 17*x*(1-x)/(1-6*x+x^2).
%o (PARI) {m=20; v=concat([17, 85], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}
%Y Second trisection of A155923. Equals 17*A001653.
%Y Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156156, A156158.
%K nonn
%O 1,1
%A _Klaus Brockhaus_, Feb 09 2009
%E Replaced abbreviation by sqrt(2) _Klaus Brockhaus_, Feb 12 2009
%E G.f. corrected by _Klaus Brockhaus_, Sep 23 2009
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