A041426 Numerators of continued fraction convergents to sqrt(229).

15, 106, 121, 227, 1710, 51527, 362399, 413926, 776325, 5848201, 176222355, 1239404686, 1415627041, 2655031727, 20000849130, 602680505627, 4238764388519, 4841444894146, 9080209282665, 68402909872801, 2061167505466695, 14496575448139666, 16557742953606361

Offset

0,1

Comments

From Johannes W. Meijer, Jun 12 2010: (Start)

The a(n) terms of this sequence can be constructed with the terms of sequence A090301.

For the terms of the periodical sequence of the continued fraction for sqrt(229) see A040213. We observe that its period is five. (End)

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, 3420, 0, 0, 0, 0, 1).

Formula

From Johannes W. Meijer, Jun 12 2010: (Start)

a(5n) = A090301(3n+1), a(5n+1) = (A090301(3n+2) - A090301(3n+1))/2, a(5n+2) = (A090301(3n+2) + A090301(3n+1))/2, a(5n+3) = A090301(3n+2) and a(5n+4) = A090301(3n+3)/2. (End)

G.f.: -(x^9-15*x^8+106*x^7-121*x^6+227*x^5+1710*x^4+227*x^3+121*x^2+106*x+15) / (x^10+3420*x^5-1). - Colin Barker, Nov 08 2013

Mathematica

Numerator[Convergents[Sqrt[229], 30]] (* Vincenzo Librandi, Nov 01 2013 *)
LinearRecurrence[{0, 0, 0, 0, 3420, 0, 0, 0, 0, 1}, {15, 106, 121, 227, 1710, 51527, 362399, 413926, 776325, 5848201}, 30] (* Harvey P. Dale, Dec 19 2016 *)

Crossrefs

Cf. A041427, A041018, A041046, A041090, A041150, A041226, A041318, A041426, A041550.

Sequence in context: A012507 A143727 A231327 * A278781 A275644 A074877

Adjacent sequences: A041423 A041424 A041425 * A041427 A041428 A041429

Keyword

nonn,frac,cofr,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 08 2013

Status

approved