A041110 Numerators of continued fraction convergents to sqrt(63).

7, 8, 119, 127, 1897, 2024, 30233, 32257, 481831, 514088, 7679063, 8193151, 122383177, 130576328, 1950451769, 2081028097, 31084845127, 33165873224, 495407070263, 528572943487, 7895428279081, 8424001222568

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,16,0,-1).

Crossrefs

Cf. A010516, A041111.

Programs

Mathematica

Numerator[Convergents[Sqrt[63], 30]] (* Vincenzo Librandi, Oct 26 2013 *)
LinearRecurrence[{0,16,0,-1},{7,8,119,127},30] (* Harvey P. Dale, Dec 17 2019 *)

Formula

a(n) = 16*a(n-2)-a(n-4). G.f.: (7+8*x+7*x^2-x^3)/(1-16*x^2+x^4). [Colin Barker, Jul 15 2012]