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A041653 Denominators of continued fraction convergents to sqrt(345). 2

%I

%S 1,1,2,5,7,47,54,155,209,364,13313,13677,26990,67657,94647,635539,

%T 730186,2095911,2826097,4922008,180018385,184940393,364958778,

%U 914857949,1279816727,8593758311,9873575038,28340908387,38214483425,66555391812,2434208588657

%N Denominators of continued fraction convergents to sqrt(345).

%H Vincenzo Librandi, <a href="/A041653/b041653.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, 13522, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^18 -x^17 +2*x^16 -5*x^15 +7*x^14 -47*x^13 +54*x^12 -155*x^11 +209*x^10 -364*x^9 -209*x^8 -155*x^7 -54*x^6 -47*x^5 -7*x^4 -5*x^3 -2*x^2 -x -1) / (x^20 -13522*x^10 +1). - _Colin Barker_, Nov 20 2013

%F a(n) = 13522*a(n-10) - a(n-20) for n>19. - _Vincenzo Librandi_, Dec 22 2013

%t Denominator[Convergents[Sqrt[345], 30]] (* _Vincenzo Librandi_, Dec 22 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,0,0,13522,0,0,0,0,0,0,0,0,0,-1},{1,1,2,5,7,47,54,155,209,364,13313,13677,26990,67657,94647,635539,730186,2095911,2826097,4922008},40] (* _Harvey P. Dale_, Oct 21 2015 *)

%o (MAGMA) I:=[1,1,2,5,7,47,54,155,209,364,13313,13677, 26990,67657,94647,635539,730186,2095911,2826097, 4922008]; [n le 20 select I[n] else 13522*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 22 2013

%Y Cf. A041652, A040326.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 20 2013

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Last modified October 23 12:19 EDT 2019. Contains 328345 sequences. (Running on oeis4.)