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%I #13 Jul 17 2023 19:01:38
%S 1,1,3,4,7,11,51,266,1115,1381,2496,3877,10250,14127,603584,617711,
%T 1839006,2456717,4295723,6752440,31305483,163279855,684424903,
%U 847704758,1532129661,2379834419,6291798499,8671632918,370500381055,379172013973
%N Denominators of continued fraction convergents to sqrt(472).
%H Vincenzo Librandi, <a href="/A041901/b041901.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 613834, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: -(x^26 -x^25 +3*x^24 -4*x^23 +7*x^22 -11*x^21 +51*x^20 -266*x^19 +1115*x^18 -1381*x^17 +2496*x^16 -3877*x^15 +10250*x^14 -14127*x^13 -10250*x^12 -3877*x^11 -2496*x^10 -1381*x^9 -1115*x^8 -266*x^7 -51*x^6 -11*x^5 -7*x^4 -4*x^3 -3*x^2 -x -1)/(x^28 -613834*x^14 +1). - _Vincenzo Librandi_, Dec 26 2013
%F a(n) = 613834*a(n-14) - a(n-28) for n>27. - _Vincenzo Librandi_, Dec 26 2013
%t Denominator[Convergents[Sqrt[472], 30]] (* or *) CoefficientList[Series[-(x^26 - x^25 + 3 x^24 - 4 x^23 + 7 x^22 - 11 x^21 + 51 x^20 - 266 x^19 + 1115 x^18 - 1381 x^17 + 2496 x^16 - 3877 x^15 + 10250 x^14 - 14127 x^13 - 10250 x^12 - 3877 x^11 - 2496 x^10 - 1381 x^9 - 1115 x^8 - 266 x^7 - 51 x^6 - 11 x^5 - 7 x^4 - 4 x^3 - 3 x^2 - x - 1)/(x^28 - 613834 x^14 + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 26 2013 *)
%o (Magma) I:=[1,1,3,4,7,11,51,266,1115,1381,2496,3877, 10250,14127,603584,617711,1839006,2456717,4295723, 6752440,31305483,163279855,684424903,847704758, 1532129661,2379834419,6291798499,8671632918]; [n le 28 select I[n] else 613834*Self(n-14)-Self(n-28): n in [1..40]]; // _Vincenzo Librandi_, Dec 26 2013
%Y Cf. A041900.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Vincenzo Librandi_, Dec 26 2013
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