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A156574 a(n) = 34*a(n-1) - a(n-2) - 4232 for n > 2; a(1)=1369, a(2)=42025.

%I A156574 #10 Jan 04 2022 21:06:52
%S A156574 1369,42025,1423249,48344209,1642275625,55789022809,1895184495649,
%T A156574 64380483825025,2187041265550969,74295022544903689,
%U A156574 2523843725261170225,85736391636334879729,2912513471910124736329,98939721653307906151225
%N A156574 a(n) = 34*a(n-1) - a(n-2) - 4232 for n > 2; a(1)=1369, a(2)=42025.
%C A156574 lim_{n -> infinity} a(n)/a(n-1) = 17+12*sqrt(2).
%H A156574 G. C. Greubel, <a href="/A156574/b156574.txt">Table of n, a(n) for n = 1..600</a>
%H A156574 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (35,-35,1).
%F A156574 a(n) = (1058 + (627 - 238*sqrt(2))*(17 + 12*sqrt(2))^n + (627 + 238*sqrt(2))*(17 - 12*sqrt(2))^n)/8.
%F A156574 G.f.: x*(1369 -5890*x +289*x^2)/((1-x)*(1-34*x+x^2)).
%F A156574 a(n) = -289*[n=0] + (529/4) + (3/4)*(209*ChebyshevU(n, 17) - 5457*ChebyshevU(n - 1, 17)). - _G. C. Greubel_, Jan 04 2022
%e A156574 a(3) = 34*a(2) - a(1) - 4232 = 34*42025 - 1369 - 4232 = 1423249.
%t A156574 LinearRecurrence[{35,-35,1}, {1369, 42025, 1423249}, 30] (* _G. C. Greubel_, Jan 04 2022 *)
%o A156574 (PARI) {m=14; v=concat([1369, 42025], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-4232); v}
%o A156574 (Sage)
%o A156574 def a(n): return -289*bool(n==0) + (529/4) + (3/4)*(209*chebyshev_U(n, 17) - 5457*chebyshev_U(n-1, 17))
%o A156574 [a(n) for n in (1..30)] # _G. C. Greubel_, Jan 04 2022
%Y A156574 Third trisection of A156572.
%Y A156574 Cf. A156164 (decimal expansion of 17+12*sqrt(2)), A156573, A156575.
%K A156574 nonn,easy
%O A156574 1,1
%A A156574 _Klaus Brockhaus_, Feb 11 2009
%E A156574 Revised by _Klaus Brockhaus_, Feb 16 2009
%E A156574 G.f. corrected by _Klaus Brockhaus_, Sep 22 2009