A042710 Numerators of continued fraction convergents to sqrt(885).

29, 30, 89, 119, 6991, 7110, 21211, 28321, 1663829, 1692150, 5048129, 6740279, 395984311, 402724590, 1201433491, 1604158081, 94242602189, 95846760270, 285936122729, 381782882999, 22429343336671, 22811126219670

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, 238, 0, 0, 0, -1).

Formula

G.f.: (29 +30*x +89*x^2 +119*x^3 +89*x^4 -30*x^5 +29*x^6 -x^7)/(1 -238*x^4 +x^8). - Vincenzo Librandi, Dec 02 2013

a(n) = 238*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 02 2013

Mathematica

Numerator[Convergents[Sqrt[885], 30]] (* or *) CoefficientList[Series[(29 + 30 x + 89 x^2 + 119 x^3 + 89 x^4 - 30 x^5 + 29 x^6 - x^7)/(1 - 238 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 02 2013 *)
LinearRecurrence[{0, 0, 0, 238, 0, 0, 0, -1}, {29, 30, 89, 119, 6991, 7110, 21211, 28321}, 30] (* Harvey P. Dale, May 15 2018 *)

Prog

(Magma) I:=[29, 30, 89, 119, 6991, 7110, 21211, 28321]; [n le 8 select I[n] else 238*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Dec 02 2013

Crossrefs

Cf. A042711.

Sequence in context: A042682 A042706 A042708 * A042704 A042702 A042714

Adjacent sequences: A042707 A042708 A042709 * A042711 A042712 A042713

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved