A042716 Numerators of continued fraction convergents to sqrt(888).

29, 30, 119, 149, 8761, 8910, 35491, 44401, 2610749, 2655150, 10576199, 13231349, 777994441, 791225790, 3151671811, 3942897601, 231839732669, 235782630270, 939187623479, 1174970253749, 69087462340921

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, 298, 0, 0, 0, -1).

Formula

G.f.: (29 +30*x +119*x^2 +149*x^3 +119*x^4 -30*x^5 +29*x^6 -x^7)/(1 -298*x^4 +x^8). - Vincenzo Librandi, Dec 02 2013

a(n) = 298*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 02 2013

Mathematica

Numerator[Convergents[Sqrt[888], 30]] (* or *) CoefficientList[Series[(29 + 30 x + 119 x^2 + 149 x^3 + 119 x^4 - 30 x^5 + 29 x^6 - x^7)/(1 - 298 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 02 2013 *)

Prog

(Magma) I:=[29, 30, 119, 149, 8761, 8910, 35491, 44401]; [n le 8 select I[n] else 298*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Dec 02 2013

Crossrefs

Cf. A042717.

Sequence in context: A042704 A042702 A042714 * A042712 A042720 A042718

Adjacent sequences: A042713 A042714 A042715 * A042717 A042718 A042719

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved