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.

A041097 Denominators of continued fraction convergents to sqrt(56).

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%I A041097 #18 Jul 09 2025 00:16:04
%S A041097 1,2,29,60,869,1798,26041,53880,780361,1614602,23384789,48384180,
%T A041097 700763309,1449910798,20999514481,43448939760,629284671121,
%U A041097 1302018282002,18857540619149,39017099520300,565096933903349,1169210967326998,16934050476481321,35037311920289640
%N A041097 Denominators of continued fraction convergents to sqrt(56).
%H A041097 Vincenzo Librandi, <a href="/A041097/b041097.txt">Table of n, a(n) for n = 0..200</a>
%H A041097 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,30,0,-1).
%F A041097 G.f.: -(x^2-2*x-1) / (x^4-30*x^2+1). - _Colin Barker_, Nov 12 2013
%F A041097 a(n) = 30*a(n-2) - a(n-4). -  _Vincenzo Librandi_, Dec 11 2013
%t A041097 Denominator[Convergents[Sqrt[56], 30]] (* _Vincenzo Librandi_, Dec 11 2013 *)
%t A041097 LinearRecurrence[{0,30,0,-1},{1,2,29,60},30] (* _Harvey P. Dale_, Dec 09 2014 *)
%o A041097 (Magma) I:=[1, 2, 29, 60]; [n le 4 select I[n] else 30*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 11 2013
%Y A041097 Cf. A041096, A040048, A020813, A010509.
%K A041097 nonn,cofr,easy,frac
%O A041097 0,2
%A A041097 _N. J. A. Sloane_
%E A041097 More terms from _Colin Barker_, Nov 12 2013