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%I #17 Sep 08 2022 08:44:55
%S 26,27,53,186,4889,14853,19742,34595,1818682,1853277,3671959,12869154,
%T 338269963,1027679043,1365949006,2393628049,125834607554,128228235603,
%U 254062843157,890416765074,23404898735081
%N Numerators of continued fraction convergents to sqrt(706).
%H Vincenzo Librandi, <a href="/A042358/b042358.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, 69190, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: (26 +27*x +53*x^2 +186*x^3 +4889*x^4 +14853*x^5 +19742*x^6 +34595*x^7 +19742*x^8 -14853*x^9 +4889*x^10 -186*x^11 +53*x^12 -27*x^13 +26*x^14 -x^15)/(1 -69190*x^8 +x^16). - _Vincenzo Librandi_, Nov 22 2013
%F a(n) = 69190*a(n-8) - a(n-16). - _Vincenzo Librandi_, Nov 22 2013
%t Numerator[Convergents[Sqrt[706], 30]] (* or *) CoefficientList[Series[(26 + 27 x + 53 x^2 + 186 x^3 + 4889 x^4 + 14853 x^5 + 19742 x^6 + 34595 x^7 + 19742 x^8 - 14853 x^9 + 4889 x^10 - 186 x^11 + 53 x^12 - 27 x^13 + 26 x^14 - x^15)/(1 - 69190 x^8 + x^16), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 22 2013 *)
%o (Magma) I:=[26,27,53,186,4889,14853,19742,34595,1818682,1853277,3671959, 12869154,338269963,1027679043,1365949006,2393628049]; [n le 16 select I[n] else 69190*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Nov 22 2013
%Y Cf. A042359.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.