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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• frac

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).

Crossrefs

Cf. A041096, A040048, A020813, A010509.

Programs

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

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 *)

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

Extensions

More terms from Colin Barker, Nov 12 2013