A041930 Numerators of continued fraction convergents to sqrt(488).

22, 243, 10714, 118097, 5206982, 57394899, 2530582538, 27893802817, 1229857906486, 13556330774163, 597708411969658, 6588348862440401, 290485058359347302, 3201923990815260723, 141175140654230819114

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,486,0,-1).

Formula

G.f.: (22 + 243*x + 22*x^2 - x^3)/(1 - 486*x^2 + x^4). - Vincenzo Librandi, Nov 12 2013

a(n) = 486*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 12 2013

Mathematica

Numerator[Convergents[Sqrt[488], 30]] (* or *) CoefficientList[Series[(22 + 243 x + 22 x^2 - x^3)/(1 - 486 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 12 2013 *)

Prog

(Magma) I:=[22, 243, 10714, 118097]; [n le 4 select I[n] else 486*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 12 2013

Crossrefs

Cf. A041931.

Sequence in context: A249089 A249090 A249091 * A249092 A125410 A200206

Adjacent sequences: A041927 A041928 A041929 * A041931 A041932 A041933

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved