A041303 Denominators of continued fraction convergents to sqrt(164).

1, 1, 5, 31, 129, 160, 3969, 4129, 20485, 127039, 528641, 655680, 16264961, 16920641, 83947525, 520605791, 2166370689, 2686976480, 66653806209, 69340782689, 344016936965, 2133442404479, 8877786554881, 11011228959360, 273147281579521, 284158510538881

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,4098,0,0,0,0,0,-1).

Formula

G.f.: -(x^10-x^9+5*x^8-31*x^7+129*x^6-160*x^5-129*x^4-31*x^3-5*x^2-x-1) / ((x^6-64*x^3-1)*(x^6+64*x^3-1)). - Colin Barker, Nov 15 2013

a(n) = 4098*a(n-6) - a(n-12). - Vincenzo Librandi, Dec 15 2013

Mathematica

Denominator[Convergents[Sqrt[164], 30]] (* Vincenzo Librandi, Dec 15 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 4098, 0, 0, 0, 0, 0, -1}, {1, 1, 5, 31, 129, 160, 3969, 4129, 20485, 127039, 528641, 655680}, 30] (* Harvey P. Dale, Nov 25 2015 *)

Prog

(Magma) I:=[1, 1, 5, 31, 129, 160, 3969, 4129, 20485, 127039, 528641, 655680]; [n le 12 select I[n] else 4098*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Crossrefs

Cf. A041302, A040151.

Sequence in context: A152122 A260045 A267938 * A184446 A077719 A235462

Adjacent sequences: A041300 A041301 A041302 * A041304 A041305 A041306

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 15 2013

Status

approved