A041995 Denominators of continued fraction convergents to sqrt(520).

1, 1, 5, 56, 229, 285, 12769, 13054, 64985, 727889, 2976541, 3704430, 165971461, 169675891, 844675025, 9461101166, 38689079689, 48150180855, 2157297037309, 2205447218164, 10979085909965, 122975392227779, 502880654821081, 625856047048860

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, 12998, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^10 -x^9 +5*x^8 -56*x^7 +229*x^6 -285*x^5 -229*x^4 -56*x^3 -5*x^2 -x -1) / ((x^6 -114*x^3 -1)*(x^6 +114*x^3 -1)). - Colin Barker, Nov 28 2013

a(n) = 12998*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Jan 12 2014

Mathematica

Denominator[Convergents[Sqrt[520], 40]] (* Vincenzo Librandi, Jan 12 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 12998, 0, 0, 0, 0, 0, -1}, {1, 1, 5, 56, 229, 285, 12769, 13054, 64985, 727889, 2976541, 3704430}, 30] (* Harvey P. Dale, Jan 30 2023 *)

Prog

(Magma) I:=[1, 1, 5, 56, 229, 285, 12769, 13054, 64985, 727889, 2976541, 3704430]; [n le 12 select I[n] else 12998*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Jan 12 2014

Crossrefs

Cf. A041994, A040497.

Sequence in context: A289259 A072318 A174514 * A288543 A062125 A030060

Adjacent sequences: A041992 A041993 A041994 * A041996 A041997 A041998

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 28 2013

Status

approved