A041829 Denominators of continued fraction convergents to sqrt(435).

1, 1, 6, 7, 286, 293, 1751, 2044, 83511, 85555, 511286, 596841, 24384926, 24981767, 149293761, 174275528, 7120314881, 7294590409, 43593266926, 50887857335, 2079107560326, 2129995417661, 12729084648631, 14859080066292, 607092287300311, 621951367366603

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, 292, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+7*x^2+1) / (x^8-292*x^4+1). - Colin Barker, Nov 25 2013

a(n) = 292*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 25 2013

Mathematica

Denominator[Convergents[Sqrt[435], 30]] (* Vincenzo Librandi, Dec 25 2013 *)
LinearRecurrence[{0, 0, 0, 292, 0, 0, 0, -1}, {1, 1, 6, 7, 286, 293, 1751, 2044}, 30] (* Harvey P. Dale, Apr 23 2022 *)

Prog

(Magma) I:=[1, 1, 6, 7, 286, 293, 1751, 2044]; [n le 8 select I[n] else 292*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 25 2013

Crossrefs

Cf. A041828, A040414.

Sequence in context: A036417 A267255 A041357 * A042497 A011315 A268508

Adjacent sequences: A041826 A041827 A041828 * A041830 A041831 A041832

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 25 2013

Status

approved