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%I #17 Sep 08 2022 08:44:55
%S 31,63,94,533,16617,83618,100235,284088,17713691,35711470,53425161,
%T 302837275,9441380686,47509740705,56951121391,161411983487,
%U 10064494097585,20290400178657,30354894276242,172064871559867,5364365912632119,26993894434720462,32358260347352581
%N Numerators of continued fraction convergents to sqrt(983).
%H Vincenzo Librandi, <a href="/A042902/b042902.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 568176, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: (31 +63*x +94*x^2 +533*x^3 +16617*x^4 +83618*x^5 +100235*x^6 +284088*x^7 +100235*x^8 -83618*x^9 +16617*x^10 -533*x^11 +94*x^12 -63*x^13 +31*x^14 -x^15)/(1 -568176*x^8 +x^16). - _Vincenzo Librandi_, Dec 09 2013
%F a(n) = 568176*a(n-8) - a(n-16). - _Vincenzo Librandi_, Dec 09 2013
%t Numerator[Convergents[Sqrt[983], 30]] (* or *) CoefficientList[Series[(31 + 63 x + 94 x^2 + 533 x^3 + 16617 x^4 + 83618 x^5 + 100235 x^6 + 284088 x^7 + 100235 x^8 - 83618 x^9 + 16617 x^10 - 533 x^11 + 94 x^12 - 63 x^13 + 31 x^14 - x^15)/(1 - 568176 x^8 + x^16), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 09 2013 *)
%o (Magma) I:=[31,63,94,533,16617,83618,100235,284088,17713691,35711470, 53425161,302837275,9441380686,47509740705,56951121391,161411983487]; [n le 16 select I[n] else 568176*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Dec 09 2013
%Y Cf. A042903.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
%E More terms from _Vincenzo Librandi_, Dec 09 2013
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