A041409 Denominators of continued fraction convergents to sqrt(219).

1, 1, 4, 5, 144, 149, 591, 740, 21311, 22051, 87464, 109515, 3153884, 3263399, 12944081, 16207480, 466753521, 482961001, 1915636524, 2398597525, 69076367224, 71474964749, 283501261471, 354976226220, 10222835595631, 10577811821851, 41956271061184

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,148,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+5*x^2+1) / (x^8-148*x^4+1). - Colin Barker, Nov 17 2013

a(n) = 148*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 17 2013

Mathematica

Denominator[Convergents[Sqrt[219], 30]] (* Vincenzo Librandi, Dec 17 2013 *)

Prog

(Magma) I:=[1, 1, 4, 5, 144, 149, 591, 740]; [n le 8 select I[n] else 148*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013

Crossrefs

Cf. A041408, A040204.

Sequence in context: A113942 A073129 A270551 * A101076 A331578 A355705

Adjacent sequences: A041406 A041407 A041408 * A041410 A041411 A041412

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 17 2013

Status

approved