A041097 Denominators of continued fraction convergents to sqrt(56).

1, 2, 29, 60, 869, 1798, 26041, 53880, 780361, 1614602, 23384789, 48384180, 700763309, 1449910798, 20999514481, 43448939760, 629284671121, 1302018282002, 18857540619149, 39017099520300, 565096933903349, 1169210967326998, 16934050476481321, 35037311920289640

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,30,0,-1).

Formula

G.f.: -(x^2-2*x-1) / (x^4-30*x^2+1). - Colin Barker, Nov 12 2013

a(n) = 30*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 11 2013

Mathematica

Denominator[Convergents[Sqrt[56], 30]] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0, 30, 0, -1}, {1, 2, 29, 60}, 30] (* Harvey P. Dale, Dec 09 2014 *)

Prog

(Magma) I:=[1, 2, 29, 60]; [n le 4 select I[n] else 30*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 11 2013

Crossrefs

Cf. A041096, A040048, A020813, A010509.

Sequence in context: A115448 A276169 A107161 * A067071 A031918 A358028

Adjacent sequences: A041094 A041095 A041096 * A041098 A041099 A041100

Keyword

nonn,cofr,easy,frac

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 12 2013

Status

approved