A042720 Numerators of continued fraction convergents to sqrt(890).

29, 30, 149, 179, 10531, 10710, 53371, 64081, 3770069, 3834150, 19106669, 22940819, 1349674171, 1372614990, 6840134131, 8212749121, 483179583149, 491392332270, 2448748912229, 2940141244499

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, 358, 0, 0, 0, -1).

Formula

G.f.: (29 +30*x +149*x^2 +179*x^3 +149*x^4 -30*x^5 +29*x^6 -x^7)/(1 -358*x^4 +x^8). - Vincenzo Librandi, Dec 02 2013

a(n) = 358*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 02 2013

Mathematica

Numerator[Convergents[Sqrt[890], 30]] (* or *) CoefficientList[Series[(29 + 30 x + 149 x^2 + 179 x^3 + 149 x^4 - 30 x^5 + 29 x^6 - x^7)/(1 - 358 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 02 2013 *)

Prog

(Magma) I:=[29, 30, 149, 179, 10531, 10710, 53371, 64081]; [n le 8 select I[n] else 358*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Dec 02 2013

Crossrefs

Cf. A042721.

Sequence in context: A042714 A042716 A042712 * A042718 A042722 A042724

Adjacent sequences: A042717 A042718 A042719 * A042721 A042722 A042723

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved