A042730 Numerators of continued fraction convergents to sqrt(895).

29, 30, 329, 359, 21151, 21510, 236251, 257761, 15186389, 15444150, 169627889, 185072039, 10903806151, 11088878190, 121792588051, 132881466241, 7828917630029, 7961799096270, 87446908592729, 95408707688999, 5621151954554671, 5716560662243670, 62786758576991371

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, 718, 0, 0, 0, -1).

Formula

G.f.: (29 +30*x +329*x^2 +359*x^3 +329*x^4 -30*x^5 +29*x^6 -x^7)/(1 -718*x^4 +x^8). - Vincenzo Librandi, Dec 03 2013

a(n) = 718*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 03 2013

Mathematica

Numerator[Convergents[Sqrt[895], 30]] (* or *) CoefficientList[Series[(29 + 30 x + 329 x^2 + 359 x^3 + 329 x^4 - 30 x^5 + 29 x^6 - x^7)/(1 - 718 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 03 2013 *)

Prog

(Magma) I:=[29, 30, 329, 359, 21151, 21510, 236251, 257761]; [n le 8 select I[n] else 718*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Dec 03 2013

Crossrefs

Cf. A042731.

Sequence in context: A042724 A042726 A042728 * A042732 A042734 A041419

Adjacent sequences: A042727 A042728 A042729 * A042731 A042732 A042733

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 03 2013

Status

approved