A041885 - OEIS

%I #18 Sep 08 2022 08:44:55

%S 1,1,2,11,13,24,37,209,246,455,19356,19811,39167,215646,254813,470459,

%T 725272,4096819,4822091,8918910,379416311,388335221,767751532,

%U 4227092881,4994844413,9221937294,14216781707,80305845829,94522627536,174828473365,7437318508866

%N Denominators of continued fraction convergents to sqrt(464).

%H Vincenzo Librandi, <a href="/A041885/b041885.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, 19602, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^18 -x^17 +2*x^16 -11*x^15 +13*x^14 -24*x^13 +37*x^12 -209*x^11 +246*x^10 -455*x^9 -246*x^8 -209*x^7 -37*x^6 -24*x^5 -13*x^4 -11*x^3 -2*x^2 -x -1) / ((x^10 -140*x^5 -1)*(x^10 +140*x^5 -1)). - _Colin Barker_, Nov 26 2013

%F a(n) = 19602*a(n-10) - a(n-20) for n>19. - _Vincenzo Librandi_, Dec 26 2013

%t Denominator[Convergents[Sqrt[464], 30]] (* _Vincenzo Librandi_, Dec 26 2013 *)

%o (Magma) I:=[1,1,2,11,13,24,37,209,246,455,19356,19811, 39167,215646,254813,470459,725272,4096819,4822091, 8918910]; [n le 20 select I[n] else 19602*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 26 2013

%Y Cf. A041884, A040442.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 26 2013