A041891 - OEIS

%I #15 Jul 17 2023 18:59:47

%S 1,1,2,3,5,18,59,1257,3830,12747,16577,29324,45901,75225,3205351,

%T 3280576,6485927,9766503,16252430,58523793,191823809,4086823782,

%U 12452295155,41443709247,53896004402,95339713649,149235718051,244575431700,10421403849451,10665979281151

%N Denominators of continued fraction convergents to sqrt(467).

%H Vincenzo Librandi, <a href="/A041891/b041891.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3251252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^26 -x^25 +2*x^24 -3*x^23 +5*x^22 -18*x^21 +59*x^20 -1257*x^19 +3830*x^18 -12747*x^17 +16577*x^16 -29324*x^15 +45901*x^14 -75225*x^13 -45901*x^12 -29324*x^11 -16577*x^10 -12747*x^9 -3830*x^8 -1257*x^7 -59*x^6 -18*x^5 -5*x^4 -3*x^3 -2*x^2 -x -1)/(x^28 -3251252*x^14 +1). - _Vincenzo Librandi_, Dec 26 2013

%F a(n) = 3251252*a(n-14) - a(n-28) for n>27. - _Vincenzo Librandi_, Dec 26 2013

%t Denominator[Convergents[Sqrt[467], 30]] (* _Harvey P. Dale_, Nov 01 2011 *)

%t CoefficientList[Series[-(x^26 - x^25 + 2 x^24 - 3 x^23 + 5 x^22 - 18 x^21 + 59 x^20 - 1257 x^19 + 3830 x^18 - 12747 x^17 + 16577 x^16 - 29324 x^15 + 45901 x^14 - 75225 x^13 - 45901 x^12 - 29324 x^11 - 16577 x^10 - 12747 x^9 - 3830 x^8 - 1257 x^7 - 59 x^6 - 18 x^5 - 5 x^4 - 3 x^3 - 2 x^2 - x - 1)/(x^28 - 3251252 x^14 + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 26 2013 *)

%o (Magma) I:=[1,1,2,3,5,18,59,1257,3830,12747,16577,29324, 45901,75225,3205351,3280576,6485927,9766503,16252430, 58523793,191823809,4086823782,12452295155,41443709247, 53896004402,95339713649,149235718051,244575431700]; [n le 28 select I[n] else 3251252*Self(n-14)-Self(n-28): n in [1..50]]; // _Vincenzo Librandi_, Dec 26 2013

%Y Cf. A041890.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Dec 26 2013