A041458 - OEIS

%I #16 Jun 15 2023 18:45:55

%S 15,16,31,47,360,2207,15809,18016,33825,51841,1589055,1640896,3229951,

%T 4870847,37325880,228826127,1639108769,1867934896,3507043665,

%U 5374978561,164756400495,170131379056,334887779551,505019158607,3870021889800,23725150497407

%N Numerators of continued fraction convergents to sqrt(245).

%H Vincenzo Librandi, <a href="/A041458/b041458.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 (0,0,0,0,0,0,0,0,0,103682,0,0,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^19 -15*x^18 +16*x^17 -31*x^16 +47*x^15 -360*x^14 +2207*x^13 -15809*x^12 +18016*x^11 -33825*x^10 -51841*x^9 -33825*x^8 -18016*x^7 -15809*x^6 -2207*x^5 -360*x^4 -47*x^3 -31*x^2 -16*x -15) / ((x^10 -322*x^5 +1)*(x^10 +322*x^5 +1)). - _Colin Barker_, Nov 18 2013

%F a(n) = 103682*a(n-10)-a(n-20). - _Wesley Ivan Hurt_, May 07 2021

%t Convergents[Sqrt[245],30]//Numerator (* or *) LinearRecurrence[{0,0,0,0,0,0,0,0,0,103682,0,0,0,0,0,0,0,0,0,-1},{15,16,31,47,360,2207,15809,18016,33825,51841,1589055,1640896,3229951,4870847,37325880,228826127,1639108769,1867934896,3507043665,5374978561},30] (* _Harvey P. Dale_, Jun 15 2023 *)

%Y Cf. A041459, A040229.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 18 2013