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 A041805 #19 Jul 09 2025 01:27:54 %S A041805 1,1,2,7,30,97,127,224,9087,9311,18398,64505,276418,893759,1170177, %T A041805 2063936,83727617,85791553,169519170,594349063,2546915422,8235095329, %U A041805 10782010751,19017106080,771466253951,790483360031,1561949613982,5476332201977,23467278421890 %N A041805 Denominators of continued fraction convergents to sqrt(423). %H A041805 Vincenzo Librandi, <a href="/A041805/b041805.txt">Table of n, a(n) for n = 0..200</a> %H A041805 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 9214, 0, 0, 0, 0, 0, 0, 0, -1). %F A041805 G.f.: -(x^14 -x^13 +2*x^12 -7*x^11 +30*x^10 -97*x^9 +127*x^8 -224*x^7 -127*x^6 -97*x^5 -30*x^4 -7*x^3 -2*x^2 -x -1) / ((x^8 -96*x^4 +1)*(x^8 +96*x^4 +1)). - _Colin Barker_, Nov 25 2013 %F A041805 a(n) = 9214*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Dec 24 2013 %t A041805 Denominator[Convergents[Sqrt[423], 30]] (* _Vincenzo Librandi_, Dec 24 2013 *) %o A041805 (Magma) I:=[1,1,2,7,30,97,127,224,9087,9311,18398,64505, 276418,893759,1170177,2063936]; [n le 16 select I[n] else 9214*Self(n-8)-Self(n-16): n in [1..50]]; // _Vincenzo Librandi_, Dec 24 2013 %Y A041805 Cf. A041804, A040402. %K A041805 nonn,frac,easy %O A041805 0,3 %A A041805 _N. J. A. Sloane_ %E A041805 More terms from _Colin Barker_, Nov 25 2013