A042748 Numerators of continued fraction convergents to sqrt(905).

30, 361, 21690, 260641, 15660150, 188182441, 11306606610, 135867461761, 8163354312270, 98096119209001, 5893930506852330, 70825262201436961, 4255409662593069990, 51135741213318276841, 3072399882461689680450

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, 722, 0, -1).

Formula

G.f.: (30 +361*x +30*x^2 -x^3)/(1 -722*x^2 +x^4). - Vincenzo Librandi, Dec 03 2013

a(n) = 722*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 03 2013

Mathematica

Numerator[Convergents[Sqrt[905], 30]] (* or *) CoefficientList[Series[(30 + 361 x + 30 x^2 - x^3)/(1 - 722 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 03 2013 *)
LinearRecurrence[{0, 722, 0, -1}, {30, 361, 21690, 260641}, 20] (* Harvey P. Dale, Mar 05 2022 *)

Prog

(Magma) I:=[30, 361, 21690, 260641]; [n le 4 select I[n] else 722*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 03 2013

Crossrefs

Cf. A042749.

Sequence in context: A086864 A138441 A058837 * A202074 A251895 A022690

Adjacent sequences: A042745 A042746 A042747 * A042749 A042750 A042751

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved