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%I #22 Nov 22 2023 16:57:37
%S 1,3,16,51,1138,3465,18463,58854,1313251,3998607,21306286,67917465,
%T 1515490516,4614389013,24587435581,78376695756,1748874742213,
%U 5325000922395,28373879354188,90446638984959,2018199937023286,6145046450054817,32743432187297371,104375343011946930
%N Denominators of continued fraction convergents to sqrt(128).
%H Vincenzo Librandi, <a href="/A041233/b041233.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1154,0,0,0,-1).
%F From _Vincenzo Librandi_, Dec 13 2013: (Start)
%F G.f.: (1+3*x+16*x^2+51*x^3-16*x^4+3*x^5-x^6)/(1-1154*x^4+x^8).
%F a(n) = 1154*a(n-4) - a(n-8). (End)
%t Denominator[Convergents[Sqrt[128], 20]] (* _Harvey P. Dale_, Apr 01 2013 *)
%t CoefficientList[Series[(1 + 3 x + 16 x^2 + 51 x^3 - 16 x^4 + 3 x^5 - x^6)/(1 - 1154 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 13 2013 *)
%o (Magma) I:=[1, 3, 16, 51, 1138, 3465, 18463, 58854]; [n le 8 select I[n] else 1154*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 13 2013
%Y Cf. A041232.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Vincenzo Librandi_, Dec 13 2013
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