A042734 Numerators of continued fraction convergents to sqrt(897).

29, 30, 569, 599, 35311, 35910, 681691, 717601, 42302549, 43020150, 816665249, 859685399, 50678418391, 51538103790, 978364286611, 1029902390401, 60712702929869, 61742605320270, 1172079598694729, 1233822204014999, 72733767431564671, 73967589635579670

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, 1198, 0, 0, 0, -1).

Formula

G.f.: (29 +30*x +569*x^2 +599*x^3 +569*x^4 -30*x^5 +29* x^6 -x^7)/(1-1198*x^4+x^8). - Vincenzo Librandi, Dec 03 2013

a(n) = 1198*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 03 2013

Mathematica

Numerator[Convergents[Sqrt[897], 30]] (* or *) CoefficientList[Series[(29 + 30 x + 569 x^2 + 599 x^3 + 569 x^4 - 30 x^5 + 29 x^6 - x^7)/(1 - 1198 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 03 2013 *)

Prog

(Magma) I:=[29, 30, 569, 599, 35311, 35910, 681691, 717601]; [n le 8 select I[n] else 1198*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Dec 03 2013

Crossrefs

Cf. A042735.

Sequence in context: A042728 A042730 A042732 * A041419 A042736 A042737

Adjacent sequences: A042731 A042732 A042733 * A042735 A042736 A042737

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 03 2013

Status

approved