A042208 Numerators of continued fraction convergents to sqrt(630).

25, 251, 12575, 126001, 6312625, 63252251, 3168925175, 31752504001, 1590794125225, 15939693756251, 798575481937775, 8001694513134001, 400883301138637825, 4016834705899512251, 201242618596114250375

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 (0,502,0,-1).

Crossrefs

Cf. A042209.

Programs

Magma

I:=[25,251,12575,126001]; [n le 4 select I[n] else 502*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 19 2013

Mathematica

Numerator[Convergents[Sqrt[630], 30]] (* or *) CoefficientList[Series[(25 + 251 x + 25 x^2 - x^3)/(x^4 - 502 x^2 + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Nov 19 2013 *)
LinearRecurrence[{0,502,0,-1},{25,251,12575,126001},20] (* Harvey P. Dale, Apr 01 2018 *)

Formula

G.f.: (25 +251*x +25*x^2 -x^3)/(x^4 -502*x^2 +1). - Vincenzo Librandi, Nov 19 2013

a(n) = 502*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 19 2013