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%I #12 Jul 17 2023 18:56:08
%S 1,2,9,29,38,105,1088,2281,3369,12388,52921,118230,5018581,10155392,
%T 45640149,147075839,192715988,532507815,5517794138,11568096091,
%U 17085890229,62825766778,268388957341,599603681460,25451743578661,51503090838782,231464106933789
%N Denominators of continued fraction convergents to sqrt(460).
%H Vincenzo Librandi, <a href="/A041877/b041877.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5071502, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: (1 +2*x +9*x^2 +29*x^3 +38*x^4 +105*x^5 +1088*x^6 +2281*x^7 +3369*x^8 +12388*x^9 +52921*x^10 +118230*x^11 -52921*x^12 +12388*x^13 -3369*x^14 +2281*x^15 -1088*x^16 +105*x^17 -38*x^18 +29*x^19 -9*x^20 +2*x^21 -x^22)/(1 -5071502*x^12 +x^24). - _Vincenzo Librandi_, Dec 26 2013
%F a(n) = 5071502*a(n-12) - a(n-24) for n>23. - _Vincenzo Librandi_, Dec 26 2013
%t Denominator[Convergents[Sqrt[460], 30]] (* or *) CoefficientList[Series[(1 + 2 x + 9 x^2 + 29 x^3 + 38 x^4 + 105 x^5 + 1088 x^6 + 2281 x^7 + 3369 x^8 + 12388 x^9 + 52921 x^10 + 118230 x^11 - 52921 x^12 + 12388 x^13 - 3369 x^14 + 2281 x^15 - 1088 x^16 + 105 x^17 - 38 x^18 + 29 x^19 - 9 x^20 + 2 x^21 - x^22)/(1 -5071502 x^12 + x^24), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 26 2013 *)
%o (Magma) I:=[1,2,9,29,38,105,1088,2281,3369,12388,52921, 118230,5018581,10155392,45640149,147075839,192715988, 532507815,5517794138,11568096091,17085890229, 62825766778,268388957341,599603681460]; [n le 24 select I[n] else 5071502*Self(n-12)-Self(n-24): n in [1..40]]; // _Vincenzo Librandi_, Dec 26 2013
%Y Cf. A041876.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Vincenzo Librandi_, Dec 26 2013
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