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%I #19 Mar 23 2023 14:09:45
%S 1,1,2,3,32,195,1982,2177,4159,6336,270271,276607,546878,823485,
%T 8781728,53513853,543920258,597434111,1141354369,1738788480,
%U 74170470529,75909259009,150079729538,225988988547,2409969615008,14685806678595,149268036400958
%N Denominators of continued fraction convergents to sqrt(469).
%H Vincenzo Librandi, <a href="/A041895/b041895.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 274430, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: -(x^18 -x^17 +2*x^16 -3*x^15 +32*x^14 -195*x^13 +1982*x^12 -2177*x^11 +4159*x^10 -6336*x^9 -4159*x^8 -2177*x^7 -1982*x^6 -195*x^5 -32*x^4 -3*x^3 -2*x^2 -x -1) / (x^20 -274430*x^10 +1). - _Colin Barker_, Nov 26 2013
%F a(n) = 274430*a(n-10) - a(n-20) for n>19. - _Vincenzo Librandi_, Dec 26 2013
%t Denominator[Convergents[Sqrt[469], 30]] (* _Vincenzo Librandi_, Dec 26 2013 *)
%t LinearRecurrence[{0,0,0,0,0,0,0,0,0,274430,0,0,0,0,0,0,0,0,0,-1},{1,1,2,3,32,195,1982,2177,4159,6336,270271,276607,546878,823485,8781728,53513853,543920258,597434111,1141354369,1738788480},30] (* _Harvey P. Dale_, Mar 23 2023 *)
%o (Magma) I:=[1,1,2,3,32,195,1982,2177,4159,6336,270271, 276607,546878,823485,8781728,53513853,543920258, 597434111,1141354369,1738788480]; [n le 20 select I[n] else 274430*Self(n-10)-Self(n-20): n in [1..50]]; // _Vincenzo Librandi_, Dec 26 2013
%Y Cf. A041894, A176443, A040447.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 26 2013
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