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

0,1

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).

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

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 *)

Crossrefs

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

Cf. A010217 (continued fraction).

Sequence in context: A010929 A022608 A060216 * A142056 A173831 A081584

Adjacent sequences: A041315 A041316 A041317 * A041319 A041320 A041321

Keyword

nonn,frac,cofr,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 08 2013

Status

approved