A041318 - OEIS

%I #22 Jul 28 2018 15:19:58

%S 13,79,92,171,1118,29239,176552,205791,382343,2499849,65378417,

%T 394770351,460148768,854919119,5589663482,146186169651,882706681388,

%U 1028892851039,1911599532427,12498490045601,326872340718053,1973732534353919,2300604875071972

%N Numerators of continued fraction convergents to sqrt(173).

%H Vincenzo Librandi, <a href="/A041318/b041318.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 2236, 0, 0, 0, 0, 1).

%F a(5*n) = A088316(3*n+1), a(5*n+1) = (A088316(3*n+2) - A088316(3*n+1))/2, a(5*n+2) = (A088316(3*n+2)+A088316(3*n+1))/2, a(5*n+3) = A088316(3*n+2) and a(5*n+4) = A088316(3*n+3)/2. [_Johannes W. Meijer_, Jun 12 2010]

%F G.f.: -(x^9-13*x^8+79*x^7-92*x^6+171*x^5+1118*x^4+171*x^3+92*x^2+79*x+13) / (x^10+2236*x^5-1). - _Colin Barker_, Nov 08 2013

%t Numerator[Convergents[Sqrt[173], 30]] (* _Vincenzo Librandi_, Nov 01 2013 *)

%t LinearRecurrence[{0,0,0,0,2236,0,0,0,0,1},{13,79,92,171,1118,29239,176552,205791,382343,2499849},30] (* _Harvey P. Dale_, Jul 28 2018 *)

%Y Cf. A041319, A041018, A041046, A041090, A041150, A041226, A041318, A041426, A041550.

%Y Cf. A010217 (continued fraction).

%K nonn,frac,cofr,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 08 2013