A042566 Numerators of continued fraction convergents to sqrt(812).

28, 57, 3220, 6497, 367052, 740601, 41840708, 84422017, 4769473660, 9623369337, 543678156532, 1096979682401, 61974540370988, 125046060424377, 7064553924136100, 14254153908696577, 805297172811144412

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, 114, 0, -1).

Formula

G.f.: (28 +57*x +28*x^2 -x^3)/(1 -114*x^2 +x^4). - Vincenzo Librandi, Nov 28 2013

a(n) = 114*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 28 2013

Mathematica

Numerator[Convergents[Sqrt[812], 30]] (* or *) CoefficientList[Series[(28 + 57 x + 28 x^2 - x^3)/(1 - 114 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 28 2013 *)
LinearRecurrence[{0, 114, 0, -1}, {28, 57, 3220, 6497}, 20] (* Harvey P. Dale, Jun 03 2024 *)

Prog

(Magma) I:=[28, 57, 3220, 6497]; [n le 4 select I[n] else 114*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 28 2013

Crossrefs

Cf. A042567.

Sequence in context: A042564 A219920 A219216 * A132769 A329306 A329307

Adjacent sequences: A042563 A042564 A042565 * A042567 A042568 A042569

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved