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Numerators of continued fraction convergents to sqrt(546).
2

%I #17 Sep 08 2022 08:44:55

%S 23,47,70,187,257,701,32503,65707,98210,262127,360337,982801,45569183,

%T 92121167,137690350,367501867,505192217,1377886301,63887962063,

%U 129153810427,193041772490,515237355407,708279127897

%N Numerators of continued fraction convergents to sqrt(546).

%H Vincenzo Librandi, <a href="/A042044/b042044.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1402,0,0,0,0,0,-1).

%F G.f.: -(x^11 - 23*x^10 + 47*x^9 - 70*x^8 + 187*x^7 -257*x^6 - 701*x^5 - 257*x^4 - 187*x^3 - 70*x^2 - 47*x - 23)/(x^12 - 1402*x^6 + 1). - _Vincenzo Librandi_, Nov 13 2013

%F a(n) = 1402*a(n-6) - a(n-12). - _Vincenzo Librandi_, Nov 14 2013

%t Numerator[Convergents[Sqrt[546], 30]] (* or *) CoefficientList[Series[-(x^11 - 23 x^10 + 47 x^9 - 70 x^8 + 187 x^7 - 257 x^6 - 701 x^5 - 257 x^4 - 187 x^3 - 70 x^2 - 47 x - 23)/(x^12 - 1402 x^6 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 14 2013 *)

%t LinearRecurrence[{0,0,0,0,0,1402,0,0,0,0,0,-1},{23,47,70,187,257,701,32503,65707,98210,262127,360337,982801},30] (* _Harvey P. Dale_, Jun 29 2021 *)

%o (Magma) I:=[23, 47, 70, 187, 257, 701, 32503, 65707, 98210, 262127, 360337, 982801]; [n le 12 select I[n] else 1402*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Nov 14 2013

%Y Cf. A042045.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.