A041607 Denominators of continued fraction convergents to sqrt(321).

1, 1, 11, 12, 419, 431, 4729, 5160, 180169, 185329, 2033459, 2218788, 77472251, 79691039, 874382641, 954073680, 33312887761, 34266961441, 375982502171, 410249463612, 14324464264979, 14734713728591, 161671601550889, 176406315279480, 6159486321053209

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, 430, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+12*x^2+1) / (x^8-430*x^4+1). - Colin Barker, Nov 19 2013

a(n) = 430*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 21 2013

Mathematica

Denominator[Convergents[Sqrt[321], 30]] (* Vincenzo Librandi Dec 21 2013 *)
LinearRecurrence[{0, 0, 0, 430, 0, 0, 0, -1}, {1, 1, 11, 12, 419, 431, 4729, 5160}, 30] (* Harvey P. Dale, Dec 24 2015 *)

Prog

(Magma) I:=[1, 1, 11, 12, 419, 431, 4729, 5160]; [n le 8 select I[n] else 430*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 21 2013

Crossrefs

Cf. A041606, A040303.

Sequence in context: A041261 A041262 A262515 * A042097 A056684 A042731

Adjacent sequences: A041604 A041605 A041606 * A041608 A041609 A041610

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 19 2013

Status

approved