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A041447 Denominators of continued fraction convergents to sqrt(239). 2

%I

%S 1,2,11,13,37,161,2452,9969,22390,32359,184185,400729,12206055,

%T 24812839,136270250,161083089,458436428,1994828801,30380868443,

%U 123518302573,277417473589,400935776162,2282096354399,4965128484960,151235950903199,307437030291358

%N Denominators of continued fraction convergents to sqrt(239).

%H Vincenzo Librandi, <a href="/A041447/b041447.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 (0,0,0,0,0,0,0,0,0,0,0,12390240,0,0,0,0,0,0,0,0,0,0,0,-1).

%F G.f.: (1 +2*x +11*x^2 +13*x^3 +37*x^4 +161*x^5 +2452*x^6 +9969*x^7 +22390*x^8 +32359*x^9 +184185*x^10 +400729*x^11 -184185*x^12 +32359*x^13 -22390*x^14 +9969*x^15 -2452*x^16 +161*x^17 -37*x^18 +13*x^19 -11*x^20 +2*x^21 -x^22)/(1 -12390240*x^12 +x^24). - _Vincenzo Librandi_, Dec 18 2013

%F a(n) = 12390240*a(n-12) - a(n-24) for n>23. - _Vincenzo Librandi_, Dec 18 2013

%t Denominator[Convergents[Sqrt[239], 30]] (* or *) CoefficientList[Series[(1 +2 x + 11 x^2 + 13 x^3 + 37 x^4 + 161 x^5 + 2452 x^6 + 9969 x^7 + 22390 x^8 + 32359 x^9 + 184185 x^10 + 400729 x^11 - 184185 x^12 + 32359 x^13 - 22390 x^14 + 9969 x^15 - 2452 x^16 + 161 x^17 - 37 x^18 + 13 x^19 - 11 x^20 + 2 x^21 - x^22)/(1 - 12390240 x^12 + x^24), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 18 2013 *)

%o (MAGMA) I:=[1,2,11,13,37,161,2452,9969,22390,32359, 184185,400729,12206055,24812839,136270250,161083089, 458436428,1994828801,30380868443,123518302573, 277417473589,400935776162,2282096354399,4965128484960]; [n le 24 select I[n] else 12390240*Self(n-12)-Self(n-24): n in [1..30]]; // _Vincenzo Librandi_, Dec 18 2013

%Y Cf. A041446.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Dec 18 2013

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Last modified October 24 04:21 EDT 2021. Contains 348217 sequences. (Running on oeis4.)