A041274 Numerators of continued fraction convergents to sqrt(150).

12, 49, 1188, 4801, 116412, 470449, 11407188, 46099201, 1117788012, 4517251249, 109531817988, 442644523201, 10733000374812, 43374646022449, 1051724504913588, 4250272665676801, 103058268481156812, 416483346590304049

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,98,0,-1).

Crossrefs

Cf. A041275.

Programs

Mathematica

Numerator[Convergents[Sqrt[150], 30]] (* Vincenzo Librandi, Nov 01 2013 *)
LinearRecurrence[{0,98,0,-1}, {12, 49, 1188, 4801}, 20] (* Bruno Berselli, Nov 01 2013 *)

Formula

a(n) = 9602*a(n-4) - a(n-8) = 98*a(n-2) - a(n-4). - Vincenzo Librandi and Bruno Berselli, Nov 01 2013

G.f.: (3 + x)*(4 + 15*x - x^2)/((1 - 10*x + x^2)*(1 + 10*x + x^2)). [Bruno Berselli, Nov 01 2013]