A042097 Denominators of continued fraction convergents to sqrt(572).

1, 1, 11, 12, 563, 575, 6313, 6888, 323161, 330049, 3623651, 3953700, 185493851, 189447551, 2079969361, 2269416912, 106473147313, 108742564225, 1193898789563, 1302641353788, 61115401063811, 62418042417599, 685295825239801, 747713867657400, 35080133737480201

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, 574, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+12*x^2+1) / ((x^4-24*x^2+1)*(x^4+24*x^2+1)). - Colin Barker, Dec 01 2013

a(n) = 574*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Jan 14 2014

Mathematica

Denominator[Convergents[Sqrt[572], 30]] (* Vincenzo Librandi, Jan 14 2014 *)
LinearRecurrence[{0, 0, 0, 574, 0, 0, 0, -1}, {1, 1, 11, 12, 563, 575, 6313, 6888}, 30] (* Harvey P. Dale, Apr 18 2022 *)

Prog

(Magma) I:=[1, 1, 11, 12, 563, 575, 6313, 6888]; [n le 8 select I[n] else 574*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Jan 14 2014

Crossrefs

Cf. A042096, A040548.

Sequence in context: A041262 A262515 A041607 * A056684 A042731 A087304

Adjacent sequences: A042094 A042095 A042096 * A042098 A042099 A042100

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 01 2013

Status

approved