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Numerators of continued fraction convergents to sqrt(867).
2

%I #20 Sep 08 2022 08:44:55

%S 29,59,265,7744,31241,70226,4104349,8278924,37220045,1087660229,

%T 4387860961,9863382151,576464025719,1162791433589,5227629760075,

%U 152764054475764,616283847663131,1385331749802026,80965525336180639

%N Numerators of continued fraction convergents to sqrt(867).

%H Vincenzo Librandi, <a href="/A042674/b042674.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, 140452, 0, 0, 0, 0, 0, -1).

%F G.f.: (29 +59*x +265*x^2 +7744*x^3 +31241*x^4 +70226*x^5 +31241*x^6 -7744*x^7 +265*x^8 -59*x^9 +29*x^10 -x^11)/(1 -140452*x^6 +x^12). - _Vincenzo Librandi_, Dec 01 2013

%F a(n) = 140452*a(n-6) - a(n-12). - _Vincenzo Librandi_, Dec 01 2013

%t Numerator[Convergents[Sqrt[867], 30]] (* or *) CoefficientList[Series[(29 + 59 x + 265 x^2 + 7744 x^3 + 31241 x^4 + 70226 x^5 + 31241 x^6 - 7744 x^7 + 265 x^8 - 59 x^9 + 29 x^10 - x^11)/(1 - 140452 x^6 + x^12), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 01 2013 *)

%o (Magma) I:=[29,59,265,7744,31241,70226,4104349,8278924,37220045,1087660229, 4387860961,9863382151]; [n le 12 select I[n] else 140452*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Dec 01 2013

%Y Cf. A042675.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.