A041266 Numerators of continued fraction convergents to sqrt(146).

12, 145, 3492, 42049, 1012668, 12194065, 293670228, 3536236801, 85163353452, 1025496478225, 24697078830852, 297390442448449, 7162067697593628, 86242202813571985, 2076974935223321268, 25009941425493427201, 602315569147065574092, 7252796771190280316305

Offset

0,1

Links

Harvey P. Dale, Table of n, a(n) for n = 0..811

Index entries for linear recurrences with constant coefficients, signature (0,290,0,-1).

Formula

G.f.: (12+145*x+12*x^2-x^3)/(1-290*x^2+x^4); // Vincenzo Librandi, Nov 01 2013

a(n) = 290*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 01 2013

Mathematica

Numerator[Convergents[Sqrt[146], 30]] (* or *) CoefficientList[Series[(12 + 145 x + 12 x^2 - x^3)/(1 - 290 x^2 + x^4), {x, 0, 25}], x] (* Vincenzo Librandi, Oct 31 2013 *)
LinearRecurrence[{0, 290, 0, -1}, {12, 145, 3492, 42049}, 20] (* Harvey P. Dale, May 11 2017 *)

Prog

(Magma) I:=[12, 145, 3492, 42049]; [n le 4 select I[n] else 290*Self(n-2)-Self(n-4): n in [1..20]]; // Vincenzo Librandi, Nov 01 2013

Crossrefs

Cf. A041267.

Sequence in context: A288792 A041061 A174227 * A015501 A039493 A196454

Adjacent sequences: A041263 A041264 A041265 * A041267 A041268 A041269

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Harvey P. Dale, May 11 2017

Status

approved