A041983 - OEIS

%I #19 Apr 18 2023 09:24:41

%S 1,1,3,67,137,204,9113,9317,27747,619751,1267249,1887000,84295249,

%T 86182249,256659747,5732696683,11722053113,17454749796,779731044137,

%U 797185793933,2374102632003,53027443697999,108428990028001,161456433726000,7212512073972001

%N Denominators of continued fraction convergents to sqrt(514).

%H Vincenzo Librandi, <a href="/A041983/b041983.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,9250,0,0,0,0,0,-1).

%F G.f.: -(x^10-x^9+3*x^8-67*x^7+137*x^6-204*x^5-137*x^4-67*x^3-3*x^2-x-1) / (x^12-9250*x^6+1). - _Colin Barker_, Nov 28 2013

%F a(n) = 9250*a(n-6) - a(n-12). - _Wesley Ivan Hurt_, Apr 18 2023

%t Denominator[Convergents[Sqrt[514], 30]] (* _Vincenzo Librandi_, Jan 11 2014 *)

%t LinearRecurrence[{0,0,0,0,0,9250,0,0,0,0,0,-1},{1,1,3,67,137,204,9113,9317,27747,619751,1267249,1887000},30] (* _Harvey P. Dale_, Sep 15 2019 *)

%o (Magma) I:=[1,1,3,67,137,204,9113,9317,27747,619751, 1267249,1887000]; [n le 12 select I[n] else 9250*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Jan 11 2014

%Y Cf. A041982, A040491.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 28 2013