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Denominators of continued fraction convergents to sqrt(58).
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%I #15 Sep 08 2022 08:44:53

%S 1,1,2,3,5,8,13,190,203,393,596,989,1585,2574,37621,40195,77816,

%T 118011,195827,313838,509665,7449148,7958813,15407961,23366774,

%U 38774735,62141509,100916244,1474968925,1575885169,3050854094,4626739263,7677593357,12304332620

%N Denominators of continued fraction convergents to sqrt(58).

%H Vincenzo Librandi, <a href="/A041101/b041101.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 (0,0,0,0,0,0,198,0,0,0,0,0,0,1).

%F G.f.: -(x^12 -x^11 +2*x^10 -3*x^9 +5*x^8 -8*x^7 +13*x^6 +8*x^5 +5*x^4 +3*x^3 +2*x^2 +x +1) / (x^14 +198*x^7 -1). - _Colin Barker_, Nov 12 2013

%F a(n) = 198*a(n-7) + a(n-14). - _Vincenzo Librandi_, Dec 11 2013

%t Denominator[Convergents[Sqrt[58], 30]] (* _Vincenzo Librandi_, Dec 11 2013 *)

%o (Magma) I:=[1, 1, 2, 3, 5, 8, 13, 190, 203, 393, 596, 989, 1585, 2574]; [n le 14 select I[n] else 198*Self(n-7)+Self(n-14): n in [1..40]]; // _Vincenzo Librandi_, Dec 11 2013

%Y Cf. A041100, A010143, A020815, A010511.

%K nonn,cofr,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 12 2013