A042728 Numerators of continued fraction convergents to sqrt(894).

29, 30, 269, 299, 17611, 17910, 160891, 178801, 10531349, 10710150, 96212549, 106922699, 6297729091, 6404651790, 57534943411, 63939595201, 3766031465069, 3829971060270, 34405799947229, 38235771007499

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, 0, 0, 598, 0, 0, 0, -1).

Formula

G.f.: (29 +30*x +269*x^2 +299*x^3 +269*x^4 -30*x^5 +29*x^6 -x^7)/(1 -598*x^4 +x^8). - Vincenzo Librandi, Dec 03 2013

a(n) = 598*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 03 2013

Mathematica

Numerator[Convergents[Sqrt[894], 30]] (* or *) CoefficientList[Series[(29 + 30 x + 269 x^2 + 299 x^3 + 269 x^4 - 30 x^5 + 29 x^6 - x^7)/(1 - 598 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 03 2013 *)
LinearRecurrence[{0, 0, 0, 598, 0, 0, 0, -1}, {29, 30, 269, 299, 17611, 17910, 160891, 178801}, 30] (* Harvey P. Dale, Jul 24 2019 *)

Prog

(Magma) I:=[29, 30, 269, 299, 17611, 17910, 160891, 178801]; [n le 8 select I[n] else 598*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Dec 03 2013

Crossrefs

Cf. A042729.

Sequence in context: A042722 A042724 A042726 * A042730 A042732 A042734

Adjacent sequences: A042725 A042726 A042727 * A042729 A042730 A042731

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved