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A042023 Denominators of continued fraction convergents to sqrt(535). 2

%I

%S 1,7,8,23,100,123,469,592,2837,6266,9103,69987,3228505,22669522,

%T 25898027,74465576,323760331,398225907,1518438052,1916663959,

%U 9185093888,20286851735,29471945623,226590471096,10452633616039,73395025783369,83847659399408,241090344582185

%N Denominators of continued fraction convergents to sqrt(535).

%H Vincenzo Librandi, <a href="/A042023/b042023.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, 3237608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^22 -7*x^21 +8*x^20 -23*x^19 +100*x^18 -123*x^17 +469*x^16 -592*x^15 +2837*x^14 -6266*x^13 +9103*x^12 -69987*x^11 -9103*x^10 -6266*x^9 -2837*x^8 -592*x^7 -469*x^6 -123*x^5 -100*x^4 -23*x^3 -8*x^2 -7*x -1)/(x^24 -3237608*x^12 +1). - _Vincenzo Librandi_, Jan 12 2014

%F a(n) = 3237608*a(n-12) - a(n-24) for n>23. - _Vincenzo Librandi_, Jan 12 2014

%t Denominator[Convergents[Sqrt[535], 30]] (* or *) CoefficientList[Series[-(x^22 - 7 x^21 + 8 x^20 - 23 x^19 + 100 x^18 - 123 x^17 + 469 x^16 - 592 x^15 + 2837 x^14 - 6266 x^13 + 9103 x^12 - 69987 x^11 - 9103 x^10 -6266 x^9 - 2837 x^8 - 592 x^7 - 469 x^6 - 123 x^5 - 100 x^4 - 23 x^3 - 8 x^2 - 7 x - 1)/(x^24 - 3237608 x^12 + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jan 12 2014 *)

%o (MAGMA) I:=[1,7,8,23,100,123,469,592,2837,6266,9103, 69987,3228505,22669522,25898027,74465576,323760331, 398225907,1518438052,1916663959,9185093888,20286851735, 29471945623,226590471096]; [n le 24 select I[n] else 3237608*Self(n-12)-Self(n-24): n in [1..30]]; // _Vincenzo Librandi_, Jan 12 2014

%Y Cf. A042022.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Jan 12 2014

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Last modified November 17 06:06 EST 2019. Contains 329217 sequences. (Running on oeis4.)