A041517 Denominators of continued fraction convergents to sqrt(275).

1, 1, 2, 5, 7, 12, 391, 403, 794, 1991, 2785, 4776, 155617, 160393, 316010, 792413, 1108423, 1900836, 61935175, 63836011, 125771186, 315378383, 441149569, 756527952, 24650044033, 25406571985, 50056616018, 125519804021, 175576420039, 301096224060

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, 0, 0, 398, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^4-x^3+2*x^2+x+1)*(x^6-6*x^3-1) / ((x^6-20*x^3+1)*(x^6+20*x^3+1)). - Colin Barker, Nov 18 2013

a(n) = 398*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 19 2013

Mathematica

Denominator[Convergents[Sqrt[275], 30]] (* Vincenzo Librandi, Dec 19 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 398, 0, 0, 0, 0, 0, -1}, {1, 1, 2, 5, 7, 12, 391, 403, 794, 1991, 2785, 4776}, 30] (* Harvey P. Dale, Jul 03 2021 *)

Prog

(Magma) I:=[1, 1, 2, 5, 7, 12, 391, 403, 794, 1991, 2785, 4776]; [n le 12 select I[n] else 398*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Dec 19 2013

Crossrefs

Cf. A041516, A040258.

Sequence in context: A041033 A134472 A041203 * A041975 A042577 A092792

Adjacent sequences: A041514 A041515 A041516 * A041518 A041519 A041520

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved