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 A041741 Denominators of continued fraction convergents to sqrt(390). 2

%I #17 Sep 08 2022 08:44:54

%S 1,1,3,4,155,159,473,632,24489,25121,74731,99852,3869107,3968959,

%T 11807025,15775984,611294417,627070401,1865435219,2492505620,

%U 96580648779,99073154399,294726957577,393800111976,15259131212665,15652931324641,46564993861947

%N Denominators of continued fraction convergents to sqrt(390).

%H Vincenzo Librandi, <a href="/A041741/b041741.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,158,0,0,0,-1).

%F G.f.: -(x^2-x-1)*(x^4+4*x^2+1) / (x^8-158*x^4+1). - _Colin Barker_, Nov 23 2013

%F a(n) = 158*a(n-4) - a(n-8) for n>7. - _Vincenzo Librandi_, Dec 23 2013

%t Denominator[Convergents[Sqrt[390], 30]] (* _Vincenzo Librandi_, Dec 23 2013 *)

%t LinearRecurrence[{0,0,0,158,0,0,0,-1},{1,1,3,4,155,159,473,632},30] (* _Harvey P. Dale_, Aug 06 2015 *)

%o (Magma) I:=[1,1,3,4,155,159,473,632]; [n le 8 select I[n] else 158*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 23 2013

%Y Cf. A041740, A040370.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 23 2013

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Last modified September 14 03:52 EDT 2024. Contains 375911 sequences. (Running on oeis4.)