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Numerators of continued fraction convergents to sqrt(97).
3

%I #14 Aug 02 2021 15:26:50

%S 9,10,59,69,128,197,325,522,847,4757,5604,105629,111233,661794,773027,

%T 1434821,2207848,3642669,5850517,9493186,53316447,62809633,1183889841,

%U 1246699474,7417387211,8664086685,16081473896,24745560581,40827034477,65572595058

%N Numerators of continued fraction convergents to sqrt(97).

%H Vincenzo Librandi, <a href="/A041174/b041174.txt">Table of n, a(n) for n = 0..200</a>

%H <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 G.f.: -(x^21 -9*x^20 +10*x^19 -59*x^18 +69*x^17 -128*x^16 +197*x^15 -325*x^14 +522*x^13 -847*x^12 +4757*x^11 +5604*x^10 +4757*x^9 +847*x^8 +522*x^7 +325*x^6 +197*x^5 +128*x^4 +69*x^3 +59*x^2 +10*x +9) / (x^22 +11208*x^11 -1). - _Colin Barker_, Nov 14 2013

%t Numerator[Convergents[Sqrt[97], 30]] (* _Vincenzo Librandi_, Oct 30 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,0,0,0,11208,0,0,0,0,0,0,0,0,0,0,1},{9,10,59,69,128,197,325,522,847,4757,5604,105629,111233,661794,773027,1434821,2207848,3642669,5850517,9493186,53316447,62809633},30] (* _Harvey P. Dale_, Aug 02 2021 *)

%Y Cf. A010548, A041175, A010168, A020854.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 14 2013