A041966 Numerators of continued fraction convergents to sqrt(506).

22, 45, 2002, 4049, 180158, 364365, 16212218, 32788801, 1458919462, 2950627725, 131286539362, 265523706449, 11814329623118, 23894182952685, 1063158379541258, 2150210942035201, 95672439829090102, 193495090600215405

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, 90, 0, -1).

Formula

G.f.: (22 + 45*x + 22*x^2 - x^3)/(1 - 90*x^2 + x^4). - Vincenzo Librandi, Nov 12 2013

a(n) = 90*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 12 2013

Mathematica

Numerator[Convergents[Sqrt[506], 30]] (* or *) CoefficientList[Series[(22 + 45 x + 22 x^2 - x^3)/(1 - 90 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 12 2013 *)

Prog

(Magma) I:=[22, 45, 2002, 4049]; [n le 4 select I[n] else 90*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 12 2013

Crossrefs

Cf. A041967.

Sequence in context: A041958 A041962 A041964 * A350321 A106838 A190614

Adjacent sequences: A041963 A041964 A041965 * A041967 A041968 A041969

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved