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Denominators of continued fraction convergents to sqrt(366).
2

%I #16 Jul 17 2023 00:31:49

%S 1,7,8,15,23,61,755,1571,2326,3897,6223,47458,1809627,12714847,

%T 14524474,27239321,41763795,110766911,1370966727,2852700365,

%U 4223667092,7076367457,11300034549,86176609300,3286011187949,23088254924943,26374266112892,49462521037835

%N Denominators of continued fraction convergents to sqrt(366).

%H Vincenzo Librandi, <a href="/A041693/b041693.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1815850, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^22 -7*x^21 +8*x^20 -15*x^19 +23*x^18 -61*x^17 +755*x^16 -1571*x^15 +2326*x^14 -3897*x^13 +6223*x^12 -47458*x^11 -6223*x^10 -3897*x^9 -2326*x^8 -1571*x^7 -755*x^6 -61*x^5 -23*x^4 -15*x^3 -8*x^2 -7*x-1)/(x^24 -1815850*x^12 +1). - _Vincenzo Librandi_, Dec 23 2013

%F a(n) = 1815850*a(n-12) - a(n-24) for n>23. - _Vincenzo Librandi_, Dec 23 2013

%t Denominator[Convergents[Sqrt[366], 30]] (* or *) CoefficientList[Series[-(x^22 - 7 x^21 + 8 x^20 - 15 x^19 + 23 x^18 - 61 x^17 + 755 x^16 - 1571 x^15 + 2326 x^14 - 3897 x^13 + 6223 x^12 - 47458 x^11 - 6223 x^10 - 3897 x^9 - 2326 x^8 - 1571 x^7 - 755 x^6 - 61 x^5 - 23 x^4 - 15 x^3 - 8 x^2 - 7 x - 1)/(x^24 - 1815850 x^12 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 23 2013 *)

%o (Magma) I:=[1,7,8,15,23,61,755,1571,2326,3897,6223,47458, 1809627,12714847,14524474,27239321,41763795,110766911, 1370966727,2852700365,4223667092,7076367457,11300034549, 86176609300]; [n le 24 select I[n] else 1815850*Self(n-12)-Self(n-24): n in [1..40]]; // _Vincenzo Librandi_, Dec 23 2013

%Y Cf. A041692.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Dec 23 2013