A042744 Numerators of continued fraction convergents to sqrt(903).

30, 601, 36090, 722401, 43380150, 868325401, 52142904210, 1043726409601, 62675727480270, 1254558276015001, 75336172288380330, 1507978004043621601, 90554016414905676390, 1812588306302157149401, 108845852394544334640450

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,1202,0,-1).

Formula

G.f.: (30 +601*x +30*x^2 -x^3)/(1 -1202*x^2 +x^4). - Vincenzo Librandi, Dec 03 2013

a(n) = 1202*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 03 2013

Mathematica

Numerator[Convergents[Sqrt[903], 30]] (* or *) CoefficientList[Series[(30 + 601 x + 30 x^2 - x^3)/(1 - 1202 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 03 2013 *)
LinearRecurrence[{0, 1202, 0, -1}, {30, 601, 36090, 722401}, 20] (* Harvey P. Dale, May 25 2022 *)

Prog

(Magma) I:=[30, 601, 36090, 722401]; [n le 4 select I[n] else 1202*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 03 2013

Crossrefs

Cf. A042745.

Sequence in context: A131206 A020982 A024436 * A020980 A051303 A020975

Adjacent sequences: A042741 A042742 A042743 * A042745 A042746 A042747

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved