cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A041095 Denominators of continued fraction convergents to sqrt(55).

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%I A041095 #18 Jul 09 2025 00:15:51
%S A041095 1,2,5,12,173,358,889,2136,30793,63722,158237,380196,5480981,11342158,
%T A041095 28165297,67672752,975583825,2018840402,5013264629,12045369660,
%U A041095 173648439869,359342249398,892332938665,2144008126728,30908446712857,63960901552442,158830249817741
%N A041095 Denominators of continued fraction convergents to sqrt(55).
%H A041095 Vincenzo Librandi, <a href="/A041095/b041095.txt">Table of n, a(n) for n = 0..200</a>
%H A041095 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,178,0,0,0,-1).
%F A041095 G.f.: -(x^2-2*x-1)*(x^4+6*x^2+1) / (x^8-178*x^4+1). - _Colin Barker_, Nov 12 2013
%F A041095 a(n) = 178*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 11 2013
%t A041095 Denominator[Convergents[Sqrt[55], 30]] (* _Vincenzo Librandi_, Dec 11 2013 *)
%t A041095 LinearRecurrence[{0,0,0,178,0,0,0,-1},{1,2,5,12,173,358,889,2136},30] (* _Harvey P. Dale_, Nov 24 2022 *)
%o A041095 (Magma) I:=[1, 2, 5, 12, 173, 358, 889, 2136]; [n le 8 select I[n] else 178*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 11 2013
%Y A041095 Cf. A041094, A010141, A010508, A020812.
%K A041095 nonn,cofr,easy,frac
%O A041095 0,2
%A A041095 _N. J. A. Sloane_
%E A041095 More terms from _Colin Barker_, Nov 12 2013