A041887 - OEIS

%I #17 Sep 08 2022 08:44:55

%S 1,1,2,7,16,39,94,321,415,736,31327,32063,63390,222233,507856,1237945,

%T 2983746,10189183,13172929,23362112,994381633,1017743745,2012125378,

%U 7054119879,16120365136,39294850151,94710065438,323425046465,418135111903,741560158368

%N Denominators of continued fraction convergents to sqrt(465).

%H Vincenzo Librandi, <a href="/A041887/b041887.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 (0,0,0,0,0,0,0,0,0,31742,0,0,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^18 -x^17 +2*x^16 -7*x^15 +16*x^14 -39*x^13 +94*x^12 -321*x^11 +415*x^10 -736*x^9 -415*x^8 -321*x^7 -94*x^6 -39*x^5 -16*x^4 -7*x^3 -2*x^2 -x -1) / (x^20 -31742*x^10 +1). - _Colin Barker_, Nov 26 2013

%F a(n) = 31742*a(n-10) - a(n-20) for n>19. - _Vincenzo Librandi_, Dec 26 2013

%t Denominator[Convergents[Sqrt[465], 30]] (* _Vincenzo Librandi_, Dec 26 2013 *)

%o (Magma) I:=[1,1,2,7,16,39,94,321,415,736,31327,32063, 63390,222233,507856,1237945,2983746,10189183,13172929, 23362112]; [n le 20 select I[n] else 31742*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 26 2013

%Y Cf. A041886, A040443.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 26 2013