A041750 Numerators of continued fraction convergents to sqrt(395).

19, 20, 139, 159, 6181, 6340, 44221, 50561, 1965539, 2016100, 14062139, 16078239, 625035221, 641113460, 4471715981, 5112829441, 198759234739, 203872064180, 1421991619819, 1625863683999, 63204811611781

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, 318, 0, 0, 0, -1).

Formula

G.f.: (19+20*x+139*x^2+159*x^3+139*x^4-20*x^5+19*x^6-x^7)/(1-318*x^4+x^8). - Vincenzo Librandi, Nov 07 2013

a(n) = 318*a(n-4)-a(n-8). - Vincenzo Librandi, Nov 07 2013

Mathematica

Numerator[Convergents[Sqrt[395], 30]] (* Harvey P. Dale, Oct 06 2011 *)
CoefficientList[Series[(19 + 20 x + 139 x^2 + 159 x^3 + 139 x^4 - 20 x^5 + 19 x^6 - x^7)/(1 - 318 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 07 2013 *)

Prog

(Magma) I:=[19, 20, 139, 159, 6181, 6340, 44221, 50561]; [n le 8 select I[n] else 318*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 07 2013

Crossrefs

Cf. A041751.

Sequence in context: A041742 A041746 A041748 * A041752 A041754 A197353

Adjacent sequences: A041747 A041748 A041749 * A041751 A041752 A041753

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved