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Denominators of continued fraction convergents to sqrt(274).
2

%I #15 Sep 08 2022 08:44:54

%S 1,1,2,9,38,47,85,2767,2852,5619,25328,106931,132259,239190,7786339,

%T 8025529,15811868,71273001,300903872,372176873,673080745,21910760713,

%U 22583841458,44494602171,200562250142,846743602739,1047305852881,1894049455620,61656888432721

%N Denominators of continued fraction convergents to sqrt(274).

%H Vincenzo Librandi, <a href="/A041515/b041515.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 (0,0,0,0,0,0,2814,0,0,0,0,0,0,1).

%F G.f.: -(x^12 -x^11 +2*x^10 -9*x^9 +38*x^8 -47*x^7 +85*x^6 +47*x^5 +38*x^4 +9*x^3 +2*x^2 +x +1) / (x^14 +2814*x^7 -1). - _Colin Barker_, Nov 18 2013

%F a(n) = 2814*a(n-7) + a(n-14) for n>13. - _Vincenzo Librandi_, Dec 19 2013

%t Denominator[Convergents[Sqrt[274], 30]] (* _Vincenzo Librandi_, Dec 19 2013 *)

%o (Magma) I:=[1,1,2,9,38,47,85,2767,2852,5619,25328, 106931,132259,239190]; [n le 14 select I[n] else 2814*Self(n-7)+Self(n-14): n in [1..30]]; // _Vincenzo Librandi_, Dec 19 2013

%Y Cf. A041514, A040257.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 18 2013