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%I #17 Sep 08 2022 08:44:54
%S 11,34,181,577,12875,39202,208885,665857,14857739,45239074,241053109,
%T 768398401,17145817931,52205852194,278175078901,886731088897,
%U 19786259034635,60245508192802,321013799998645
%N Numerators of continued fraction convergents to sqrt(128).
%H Vincenzo Librandi and Bruno Berselli, <a href="/A041232/b041232.txt">Table of n, a(n) for n = 0..200</a> (first 151 terms from Vincenzo Librandi).
%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 G.f.: (11 +34*x +181*x^2 +577*x^3 +181*x^4 -34*x^5 +11*x^6 -x^7) / ((1 -6*x +x^2)*(1 +6*x +x^2)*(1 +34*x^2 +x^4)). [_Bruno Berselli_, Oct 31 2013]
%t Numerator[Convergents[Sqrt[128], 30]] (* _Vincenzo Librandi_, Oct 31 2013 *)
%t LinearRecurrence[{0, 0, 0, 1154, 0, 0, 0, -1}, {11, 34, 181, 577, 12875, 39202, 208885, 665857}, 30] (* _Bruno Berselli_, Oct 31 2013 *)
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((11+34*x+181*x^2+577*x^3+181*x^4-34*x^5+11*x^6-x^7)/((1-6*x+x^2)*(1+6*x+x^2)*(1+34*x^2+x^4)))); // _Bruno Berselli_, Oct 31 2013
%Y Cf. A041233.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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