A041969 Denominators of continued fraction convergents to sqrt(507).

1, 1, 2, 29, 31, 60, 2671, 2731, 5402, 78359, 83761, 162120, 7217041, 7379161, 14596202, 211725989, 226322191, 438048180, 19500442111, 19938490291, 39438932402, 572083543919, 611522476321, 1183606020240, 52690187366881, 53873793387121, 106563980754002

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, 2702, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^4 -x^3 +2*x^2 +x +1)*(x^6 -30*x^3 -1) / ((x^2 -4*x +1)*(x^2 +4*x +1)*(x^4 -4*x^3 +15*x^2 -4*x +1)*(x^4 +4*x^3 +15*x^2 +4*x +1)). - Colin Barker, Nov 28 2013

a(n) = 2702*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 28 2013

Mathematica

Denominator[Convergents[Sqrt[507], 30]] (* Vincenzo Librandi, Dec 28 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 2702, 0, 0, 0, 0, 0, -1}, {1, 1, 2, 29, 31, 60, 2671, 2731, 5402, 78359, 83761, 162120}, 30] (* Harvey P. Dale, Mar 25 2018 *)

Prog

(Magma) I:=[1, 1, 2, 29, 31, 60, 2671, 2731, 5402, 78359, 83761, 162120]; [n le 12 select I[n] else 2702*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 28 2013

Crossrefs

Cf. A041968, A040484.

Sequence in context: A089536 A019379 A107166 * A295386 A019392 A060503

Adjacent sequences: A041966 A041967 A041968 * A041970 A041971 A041972

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 28 2013

Status

approved