A041325 Denominators of continued fraction convergents to sqrt(176).

1, 3, 4, 15, 394, 1197, 1591, 5970, 156811, 476403, 633214, 2376045, 62410384, 189607197, 252017581, 945659940, 24839176021, 75463188003, 100302364024, 376370280075, 9885929645974, 30034159217997, 39920088863971, 149794425809910, 3934575159921631

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,398,0,0,0,-1).

Formula

G.f.: -(x^2-3*x-1)*(x^4+5*x^2+1) / ((x^4-20*x^2+1)*(x^4+20*x^2+1)). - Colin Barker, Nov 15 2013

a(n) = 398*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 15 2013

Mathematica

Denominator[Convergents[Sqrt[176], 30]] (* Vincenzo Librandi, Dec 15 2013 *)
LinearRecurrence[{0, 0, 0, 398, 0, 0, 0, -1}, {1, 3, 4, 15, 394, 1197, 1591, 5970}, 30] (* Harvey P. Dale, Apr 30 2023 *)

Prog

(Magma) I:=[1, 3, 4, 15, 394, 1197, 1591, 5970]; [n le 8 select I[n] else 398*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Crossrefs

Cf. A041324, A010220.

Sequence in context: A346974 A354395 A103095 * A042541 A325212 A329890

Adjacent sequences: A041322 A041323 A041324 * A041326 A041327 A041328

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 15 2013

Status

approved