A041204 - OEIS

%I #15 Sep 26 2020 19:55:06

%S 10,11,21,32,85,202,287,489,776,16009,16785,32794,49579,131952,313483,

%T 445435,758918,1204353,24845978,26050331,50896309,76946640,204789589,

%U 486525818,691315407,1177841225,1869156632,38560973865,40430130497,78991104362,119421234859

%N Numerators of continued fraction convergents to sqrt(113).

%H Vincenzo Librandi, <a href="/A041204/b041204.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 (0,0,0,0,0,0,0,0,1552,0,0,0,0,0,0,0,0,1).

%F G.f.: -(x^17 -10*x^16 +11*x^15 -21*x^14 +32*x^13 -85*x^12 +202*x^11 -287*x^10 +489*x^9 +776*x^8 +489*x^7 +287*x^6 +202*x^5 +85*x^4 +32*x^3 +21*x^2 +11*x +10) / (x^18 +1552*x^9 -1). - _Colin Barker_, Nov 08 2013

%t Numerator[Convergents[Sqrt[113], 30]] (* _Vincenzo Librandi_, Oct 31 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,0,1552,0,0,0,0,0,0,0,0,1},{10,11,21,32,85,202,287,489,776,16009,16785,32794,49579,131952,313483,445435,758918,1204353},40] (* _Harvey P. Dale_, Sep 26 2020 *)

%Y Cf. A041205.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 08 2013