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A042040 Numerators of continued fraction convergents to sqrt(544). 2

%I #23 Sep 08 2022 08:44:55

%S 23,70,793,2449,113447,342790,3884137,11995201,555663383,1678985350,

%T 19024502233,58752492049,2721639136487,8223669901510,93182008053097,

%U 287769694060801,13330587934849943,40279533498610630

%N Numerators of continued fraction convergents to sqrt(544).

%H Vincenzo Librandi, <a href="/A042040/b042040.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,4898,0,0,0,-1).

%F G.f.: (23 +70*x +793*x^2 +2449*x^3 +793*x^4 -70*x^5 +23*x^6 -x^7) / ((1 -70*x^2 +x^4)*(1 +70*x^2 +x^4)). - _Vincenzo Librandi_, Nov 13 2013

%F a(n) = 4898*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 14 2013

%t Numerator[Convergents[Sqrt[544], 30]] (* or *) CoefficientList[Series[(23 + 70 x + 793 x^2 + 2449 x^3 + 793 x^4 - 70 x^5 + 23 x^6 - x^7)/(1 - 4898 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 14 2013 *)

%t LinearRecurrence[{0,0,0,4898,0,0,0,-1},{23,70,793,2449,113447,342790,3884137,11995201},20] (* _Harvey P. Dale_, Jul 27 2020 *)

%o (Magma) I:=[23,70,793,2449,113447,342790,3884137,11995201]; [n le 8 select I[n] else 4898*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 14 2013

%Y Cf. A042041.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.

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Last modified June 20 03:21 EDT 2024. Contains 373512 sequences. (Running on oeis4.)