A042093 Denominators of continued fraction convergents to sqrt(570).

1, 1, 7, 8, 375, 383, 2673, 3056, 143249, 146305, 1021079, 1167384, 54720743, 55888127, 390049505, 445937632, 20903180577, 21349118209, 148997889831, 170347008040, 7984960259671, 8155307267711, 56916803865937, 65072111133648, 3050233916013745

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,382,0,0,0,-1).

Formula

G.f.: (1 + x - x^2)*(1 + 8*x^2 + x^4)/(1 - 382*x^4 + x^8). - Colin Barker, Dec 01 2013

a(n) = 382*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Jan 14 2014

Mathematica

Denominator[Convergents[Sqrt[570], 30]] (* Vincenzo Librandi, Jan 14 2014 *)
LinearRecurrence[{0, 0, 0, 382, 0, 0, 0, -1}, {1, 1, 7, 8, 375, 383, 2673, 3056}, 30] (* Harvey P. Dale, Jun 02 2017 *)

Prog

(Magma) I:=[1, 1, 7, 8, 375, 383, 2673, 3056]; [n le 8 select I[n] else 382*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Jan 14 2014

Crossrefs

Cf. A042092, A040546.

Sequence in context: A371104 A041473 A041751 * A042499 A156206 A226487

Adjacent sequences: A042090 A042091 A042092 * A042094 A042095 A042096

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 01 2013

Status

approved