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.
%I A041305 #18 Jul 09 2025 00:36:22 %S A041305 1,1,6,13,71,84,2087,2171,12942,28055,153217,181272,4503745,4685017, %T A041305 27928830,60542677,330642215,391184892,9719079623,10110264515, %U A041305 60270402198,130651068911,713525746753,844176815664,20973769322689,21817946138353 %N A041305 Denominators of continued fraction convergents to sqrt(165). %H A041305 Vincenzo Librandi, <a href="/A041305/b041305.txt">Table of n, a(n) for n = 0..200</a> %H A041305 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,2158,0,0,0,0,0,-1). %F A041305 G.f.: -(x^10 -x^9 +6*x^8 -13*x^7 +71*x^6 -84*x^5 -71*x^4 -13*x^3 -6*x^2 -x -1) / ((x^4 -13*x^2 +1)*(x^8 +13*x^6 +168*x^4 +13*x^2 +1)). - _Colin Barker_, Nov 15 2013 %F A041305 a(n) = 2158*a(n-6) - a(n-12). - _Vincenzo Librandi_, Dec 15 2013 %t A041305 Denominator[Convergents[Sqrt[165], 30]] (* _Vincenzo Librandi_, Dec 15 2013 *) %o A041305 (Magma) I:=[1,1,6,13,71,84,2087,2171,12942,28055,153217, 181272]; [n le 12 select I[n] else 2158*Self(n-6)-Self(n-12): n in [1..40]]; // _Vincenzo Librandi_, Dec 15 2013 %Y A041305 Cf. A041304, A010213, A178592. %K A041305 nonn,frac,easy %O A041305 0,3 %A A041305 _N. J. A. Sloane_ %E A041305 More terms from _Colin Barker_, Nov 15 2013