A041813 Denominators of continued fraction convergents to sqrt(427).

1, 1, 2, 3, 122, 125, 247, 372, 15127, 15499, 30626, 46125, 1875626, 1921751, 3797377, 5719128, 232562497, 238281625, 470844122, 709125747, 28835874002, 29544999749, 58380873751, 87925873500, 3575415813751, 3663341687251, 7238757501002, 10902099188253

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, 124, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+3*x^2+1) / (x^8-124*x^4+1). - Colin Barker, Nov 25 2013

a(n) = 124*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 24 2013

Mathematica

Denominator[Convergents[Sqrt[427], 30]] (* Vincenzo Librandi, Dec 24 2013 *)
LinearRecurrence[{0, 0, 0, 124, 0, 0, 0, -1}, {1, 1, 2, 3, 122, 125, 247, 372}, 30] (* Harvey P. Dale, Jan 20 2019 *)

Prog

(Magma) I:=[1, 1, 2, 3, 122, 125, 247, 372]; [n le 8 select I[n] else 124*Self(n-4)-Self(n-8): n in [1..50]]; // Vincenzo Librandi, Dec 24 2013

Crossrefs

Cf. A041812, A040406.

Sequence in context: A152838 A208247 A102697 * A065842 A065841 A051177

Adjacent sequences: A041810 A041811 A041812 * A041814 A041815 A041816

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 25 2013

Status

approved