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%I #18 Apr 18 2024 09:35:28
%S 25,137,797,4645,27073,157793,919685,5360317,31242217,182092985,
%T 1061315693,6185801173,36053491345,210135146897,1224757390037,
%U 7138409193325,41605697769913,242495777426153,1413368966787005
%N a(n) = 6*a(n-1) - a(n-2) for n > 2; a(1) = 25, a(2) = 137.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-1).
%F a(n) = ((26+7*sqrt(2))*(3-2*sqrt(2))^n+(26-7*sqrt(2))*(3+2*sqrt(2))^n)/4.
%F G.f.: x*(25-13*x)/(1-6*x+x^2).
%F Limit_{n -> oo} a(n)/a(n-1) = 3+2*sqrt(2).
%t LinearRecurrence[{6,-1},{25,137},30] (* _Harvey P. Dale_, Jan 02 2019 *)
%o (PARI) {m=19; v=concat([25,137], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}
%Y Third trisection of A155923.
%Y Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156156, A156157.
%K nonn,easy,changed
%O 1,1
%A _Klaus Brockhaus_, Feb 09 2009
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