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 A041175 #17 Jul 09 2025 00:23:22 %S A041175 1,1,6,7,13,20,33,53,86,483,569,10725,11294,67195,78489,145684,224173, %T A041175 369857,594030,963887,5413465,6377352,120205801,126583153,753121566, %U A041175 879704719,1632826285,2512531004,4145357289,6657888293,10803245582,60674116203,71477361785 %N A041175 Denominators of continued fraction convergents to sqrt(97). %H A041175 Vincenzo Librandi, <a href="/A041175/b041175.txt">Table of n, a(n) for n = 0..200</a> %H A041175 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,11208,0,0,0,0,0,0,0,0,0,0,1). %F A041175 G.f.: -(x^20 -x^19 +6*x^18 -7*x^17 +13*x^16 -20*x^15 +33*x^14 -53*x^13 +86*x^12 -483*x^11 +569*x^10 +483*x^9 +86*x^8 +53*x^7 +33*x^6 +20*x^5 +13*x^4 +7*x^3 +6*x^2 +x +1) / (x^22 +11208*x^11 -1). - _Colin Barker_, Nov 14 2013 %F A041175 a(n) = 11208*a(n-11) + a(n-22). - _Vincenzo Librandi_, Dec 12 2013 %t A041175 Denominator[Convergents[Sqrt[97], 30]] (* _Vincenzo Librandi_, Dec 12 2013 *) %o A041175 (Magma) I:=[1, 1, 6, 7, 13, 20, 33, 53, 86, 483, 569, 10725, 11294, 67195, 78489, 145684, 224173, 369857, 594030, 963887, 5413465, 6377352]; [n le 22 select I[n] else 11208*Self(n-11)+Self(n-22): n in [1..40]]; // _Vincenzo Librandi_, Dec 12 2013 %Y A041175 Cf. A041174, A010168, A020854, A010548. %K A041175 nonn,frac,easy %O A041175 0,3 %A A041175 _N. J. A. Sloane_ %E A041175 More terms from _Colin Barker_, Nov 14 2013