A042576 - OEIS

%I #19 Sep 08 2022 08:44:55

%S 28,29,57,143,200,343,19408,19751,39159,98069,137228,235297,13313860,

%T 13549157,26863017,67275191,94138208,161413399,9133288552,9294701951,

%U 18427990503,46150682957,64578673460

%N Numerators of continued fraction convergents to sqrt(817).

%H Vincenzo Librandi, <a href="/A042576/b042576.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, 686, 0, 0, 0, 0, 0, -1).

%F G.f.: (28 +29*x +57*x^2 +143*x^3 +200*x^4 +343*x^5 +200*x^6 -143*x^7 +57*x^8 -29*x^9 +28*x^10 -x^11)/(1 -686*x^6 +x^12). - _Vincenzo Librandi_, Nov 28 2013

%F a(n) = 686*a(n-6) - a(n-12). - _Vincenzo Librandi_, Nov 28 2013

%t Numerator[Convergents[Sqrt[817], 30]] (* or *) CoefficientList[Series[(28 + 29 x + 57 x^2 + 143 x^3 + 200 x^4 + 343 x^5 + 200 x^6 - 143 x^7 + 57 x^8 - 29 x^9 + 28 x^10 - x^11)/(1 - 686 x^6 + x^12), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 28 2013 *)

%t LinearRecurrence[{0,0,0,0,0,686,0,0,0,0,0,-1},{28,29,57,143,200,343,19408,19751,39159,98069,137228,235297},30] (* _Harvey P. Dale_, Jan 17 2017 *)

%o (Magma) I:=[28,29,57,143,200,343,19408,19751,39159,98069,137228,235297]; [n le 12 select I[n] else 686*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Nov 28 2013

%Y Cf. A042577.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.