A041267 Denominators of continued fraction convergents to sqrt(146).

1, 12, 289, 3480, 83809, 1009188, 24304321, 292661040, 7048169281, 84870692412, 2043944787169, 24612208138440, 592736940109729, 7137455489455188, 171891668687034241, 2069837479733866080, 49847991182299820161, 600245731667331708012

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,290,0,-1).

Formula

G.f.: (1 +12*x -x^2)/(x^4 -290*x^2 +1). - Vincenzo Librandi, Dec 14 2013

a(n) = 290*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 14 2013

Mathematica

Denominator[Convergents[Sqrt[146], 30]] (* or *) CoefficientList[Series[(1 + 12 x - x^2)/(x^4 - 290 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 14 2013 *)
LinearRecurrence[{0, 290, 0, -1}, {1, 12, 289, 3480}, 20] (* Harvey P. Dale, Jan 20 2021 *)

Prog

(Magma) I:=[1, 12, 289, 3480]; [n le 4 select I[n] else 290*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 14 2013

Crossrefs

Cf. A041266.

Sequence in context: A321938 A001164 A226100 * A041264 A220307 A361302

Adjacent sequences: A041264 A041265 A041266 * A041268 A041269 A041270

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 14 2013

Status

approved