A042649 Denominators of continued fraction convergents to sqrt(854).

1, 4, 9, 103, 421, 4734, 9889, 44290, 2578709, 10359126, 23296961, 266625697, 1089799749, 12254422936, 25598645621, 114649005420, 6675240959981, 26815612845344, 60306466650669, 690186746002703, 2821053450661481, 31721774703278994, 66264602857219469

Offset

0,2

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, 0, 0, 0, 2588598, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^14 -4*x^13 +9*x^12 -103*x^11 +421*x^10 -4734*x^9 +9889*x^8 -44290*x^7 -9889*x^6 -4734*x^5 -421*x^4 -103*x^3 -9*x^2 -4*x -1) / (x^16 -2588598*x^8 +1). - Colin Barker, Dec 20 2013

Mathematica

Denominator[Convergents[Sqrt[854], 30]] (* Vincenzo Librandi, Jan 26 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 2588598, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 4, 9, 103, 421, 4734, 9889, 44290, 2578709, 10359126, 23296961, 266625697, 1089799749, 12254422936, 25598645621, 114649005420}, 30] (* Harvey P. Dale, Dec 15 2024 *)

Crossrefs

Cf. A042648, A040824.

Sequence in context: A061090 A061272 A117680 * A324024 A042381 A230743

Adjacent sequences: A042646 A042647 A042648 * A042650 A042651 A042652

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 20 2013

Status

approved