A041826 Numerators of continued fraction convergents to sqrt(434).

20, 21, 104, 125, 5104, 5229, 26020, 31249, 1275980, 1307229, 6504896, 7812125, 318989896, 326802021, 1626197980, 1953000001, 79746198020, 81699198021, 406542990104, 488242188125, 19936230515104, 20424472703229

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,250,0,0,0,-1).

Formula

G.f.: (20 + 21*x + 104*x^2 + 125*x^3 + 104*x^4 - 21*x^5 + 20*x^6 - x^7)/(1 - 250*x^4 + x^8). - Vincenzo Librandi, Nov 09 2013

a(n) = 250*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 09 2013

Mathematica

Numerator[Convergents[Sqrt[434], 30]] (* or *) CoefficientList[Series[(20 + 21 x + 104 x^2 + 125 x^3 + 104 x^4 - 21 x^5 + 20 x^6 - x^7)/(1 - 250 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 09 2013 *)

Prog

(Magma) I:=[20, 21, 104, 125, 5104, 5229, 26020, 31249]; [n le 8 select I[n] else 250*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Nov 09 2013

Crossrefs

Cf. A041827.

Sequence in context: A041822 A041820 A329599 * A041824 A309829 A037308

Adjacent sequences: A041823 A041824 A041825 * A041827 A041828 A041829

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane

Status

approved