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A041663 Denominators of continued fraction convergents to sqrt(350). 2

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

%S 1,1,3,7,17,24,881,905,2691,6287,15265,21552,791137,812689,2416515,

%T 5645719,13707953,19353672,710440145,729793817,2170027779,5069849375,

%U 12309726529,17379575904,637974459073,655354034977,1948682529027,4552719093031,11054120715089

%N Denominators of continued fraction convergents to sqrt(350).

%H Vincenzo Librandi, <a href="/A041663/b041663.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 (0,0,0,0,0,898,0,0,0,0,0,-1).

%F G.f.: -(x^10-x^9+3*x^8-7*x^7+17*x^6-24*x^5-17*x^4-7*x^3-3*x^2-x-1) / ((x^6-30*x^3+1)*(x^6+30*x^3+1)). - _Colin Barker_, Nov 21 2013

%F a(n) = 898*a(n-6) - a(n-12) for n>11. - _Vincenzo Librandi_, Dec 22 2013

%t Denominator[Convergents[Sqrt[350], 30]] (* _Vincenzo Librandi_, Dec 22 2013 *)

%o (Magma) I:=[1,1,3,7,17,24,881,905,2691,6287,15265,21552]; [n le 12 select I[n] else 898*Self(n-6)-Self(n-12): n in [1..40]]; // _Vincenzo Librandi_, Dec 22 2013

%Y Cf. A041662, A040331.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 21 2013

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)