A041318 Numerators of continued fraction convergents to sqrt(173).

13, 79, 92, 171, 1118, 29239, 176552, 205791, 382343, 2499849, 65378417, 394770351, 460148768, 854919119, 5589663482, 146186169651, 882706681388, 1028892851039, 1911599532427, 12498490045601, 326872340718053, 1973732534353919, 2300604875071972

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• cofr
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 2236, 0, 0, 0, 0, 1).

Crossrefs

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

Cf. A010217 (continued fraction).

Programs

Mathematica

Numerator[Convergents[Sqrt[173], 30]] (* Vincenzo Librandi, Nov 01 2013 *)
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 *)

Formula

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]

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

Extensions

More terms from Colin Barker, Nov 08 2013