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A041955 Denominators of continued fraction convergents to sqrt(500). 2

%I

%S 1,2,3,11,25,36,61,646,707,1353,3413,11592,15005,41602,1845493,

%T 3732588,5578081,20466831,46511743,66978574,113490317,1201881744,

%U 1315372061,2517253805,6349879671,21566892818,27916772489,77400437796,3433536035513,6944472508822

%N Denominators of continued fraction convergents to sqrt(500).

%H Vincenzo Librandi, <a href="/A041955/b041955.txt">Table of n, a(n) for n = 0..200</a>

%F G.f.: -(x^26 -2*x^25 +3*x^24 -11*x^23 +25*x^22 -36*x^21 +61*x^20 -646*x^19 +707*x^18 -1353*x^17 +3413*x^16 -11592*x^15 +15005*x^14 -41602*x^13 -15005*x^12 -11592*x^11 -3413*x^10 -1353*x^9 -707*x^8 -646*x^7 -61*x^6 -36*x^5 -25*x^4 -11*x^3 -3*x^2 -2*x -1)/(x^28 -1860498*x^14 +1). - _Vincenzo Librandi_, Dec 27 2013

%F a(n) = 1860498*a(n-14) - a(n-28) for n>27. - _Vincenzo Librandi_, Dec 27 2013

%t Denominator[Convergents[Sqrt[500], 30]] (* or *) CoefficientList[Series[-(x^26 - 2 x^25 + 3 x^24 - 11 x^23 + 25 x^22 - 36 x^21 + 61 x^20 - 646 x^19 + 707 x^18 - 1353 x^17 + 3413 x^16 - 11592 x^15 + 15005 x^14 - 41602 x^13 - 15005 x^12 - 11592 x^11 - 3413 x^10 - 1353 x^9 - 707 x^8 - 646 x^7 - 61 x^6 - 36 x^5 - 25 x^4 - 11 x^3 - 3 x^2 - 2 x - 1)/(x^28 - 1860498 x^14 + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 27 2013 *)

%o (MAGMA) I:=[1,2,3,11,25,36,61,646,707,1353,3413,11592, 15005,41602,1845493,3732588,5578081,20466831,46511743, 66978574,113490317,1201881744,1315372061,2517253805, 6349879671,21566892818,27916772489,77400437796]; [n le 28 select I[n] else 1860498*Self(n-14)-Self(n-28): n in [1..40]]; // _Vincenzo Librandi_, Dec 27 2013

%Y Cf. A041954.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Vincenzo Librandi_, Dec 27 2013

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Last modified May 17 19:51 EDT 2022. Contains 353778 sequences. (Running on oeis4.)