A041852 Numerators of continued fraction convergents to sqrt(448).

21, 127, 5355, 32257, 1360149, 8193151, 345472491, 2081028097, 87748652565, 528572943487, 22287812279019, 134255446617601, 5661016570218261, 34100354867927167, 1437875921023159275

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,254,0,-1).

Formula

G.f.: (21 + 127*x + 21*x^2 - x^3)/(1 - 254*x^2 + x^4). - Vincenzo Librandi, Nov 10 2013

a(n) = 254*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 10 2013

Mathematica

Numerator[Convergents[Sqrt[448], 30]] (* or *) CoefficientList[Series[(21 + 127 x + 21 x^2 - x^3)/(1 - 254 x^2 + x^4), {x, 0, 25}], x] (* Vincenzo Librandi, Nov 10 2013 *)

Prog

(Magma) I:=[21, 127, 5355, 32257]; [n le 4 select I[n] else 254*Self(n-2)-Self(n-4): n in [1..20]]; // Vincenzo Librandi, Nov 10 2013

Crossrefs

Cf. A041853.

Sequence in context: A316310 A317265 A213565 * A220712 A295916 A124117

Adjacent sequences: A041849 A041850 A041851 * A041853 A041854 A041855

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved