A041513 Denominators of continued fraction convergents to sqrt(273).

1, 1, 2, 21, 23, 44, 1431, 1475, 2906, 30535, 33441, 63976, 2080673, 2144649, 4225322, 44397869, 48623191, 93021060, 3025297111, 3118318171, 6143615282, 64554470991, 70698086273, 135252557264, 4398779918721, 4534032475985, 8932812394706, 93862156423045

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1454,0,0,0,0,0,-1).

Formula

G.f.: -(x^4-x^3+2*x^2+x+1)*(x^6-22*x^3-1) / (x^12-1454*x^6+1). - Colin Barker, Nov 18 2013

a(n) = 1454*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 19 2013

Mathematica

Denominator[Convergents[Sqrt[273], 30]] (* Vincenzo Librandi, Dec 19 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 1454, 0, 0, 0, 0, 0, -1}, {1, 1, 2, 21, 23, 44, 1431, 1475, 2906, 30535, 33441, 63976}, 30] (* Harvey P. Dale, Jun 15 2021 *)

Prog

(Magma) I:=[1, 1, 2, 21, 23, 44, 1431, 1475, 2906, 30535, 33441, 63976]; [n le 12 select I[n] else 1454*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Dec 19 2013

Crossrefs

Cf. A041512, A040256.

Sequence in context: A233135 A322925 A294116 * A135053 A042565 A079907

Adjacent sequences: A041510 A041511 A041512 * A041514 A041515 A041516

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved