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 A042292 Numerators of continued fraction convergents to sqrt(672). 2

%I #12 Sep 08 2022 08:44:55

%S 25,26,311,337,17161,17498,209639,227137,11566489,11793626,141296375,

%T 153090001,7795796425,7948886426,95233547111,103182433537,

%U 5254355223961,5357537657498,64187269456439

%N Numerators of continued fraction convergents to sqrt(672).

%H Vincenzo Librandi, <a href="/A042292/b042292.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 (0,0,0,674,0,0,0,-1).

%F G.f.: (25 +26*x +311*x^2 +337*x^3 +311*x^4 -26*x^5 +25*x^6 -x^7)/(1 -674*x^4 +x^8). - _Vincenzo Librandi_, Nov 21 2013

%F a(n) = 674*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 21 2013

%t Numerator[Convergents[Sqrt[672], 30]] (* or *) CoefficientList[Series[(25 + 26 x + 311 x^2 + 337 x^3 + 311 x^4 - 26 x^5 + 25 x^6 - x^7)/(1 - 674 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 21 2013 *)

%o (Magma) I:=[25, 26, 311, 337, 17161, 17498, 209639, 227137]; [n le 8 select I[n] else 674*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 21 2013

%Y Cf. A042293.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

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Last modified July 19 14:25 EDT 2024. Contains 374394 sequences. (Running on oeis4.)