A042736 Numerators of continued fraction convergents to sqrt(898).

29, 30, 869, 899, 53011, 53910, 1562491, 1616401, 95313749, 96930150, 2809357949, 2906288099, 171374067691, 174280355790, 5051224029811, 5225504385601, 308130478394669, 313355982780270, 9082097996242229, 9395453979022499, 554018428779547171

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1798,0,0,0,-1).

Formula

G.f.: (29 +30*x +869*x^2 +899*x^3 +869*x^4 -30*x^5 +29*x^6 - x^7)/(1 -1798*x^4 +x^8). - Vincenzo Librandi, Dec 03 2013, simplified by Colin Barker, Dec 27 2013

a(n) = 1798*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 03 2013, simplified by Colin Barker, Dec 27 2013

Mathematica

Numerator[Convergents[Sqrt[898], 30]] (* or *) CoefficientList[Series[(29 + 30 x + 869 x^2 + 899 x^3 + 869 x^4 - 30 x^5 + 29 x^6 - x^7)/(1 - 1798 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 03 2013 *)
LinearRecurrence[{0, 0, 0, 1798, 0, 0, 0, -1}, {29, 30, 869, 899, 53011, 53910, 1562491, 1616401}, 30] (* Harvey P. Dale, Mar 03 2018 *)

Prog

(Magma) I:=[29, 30, 869, 899, 53011, 53910, 1562491, 1616401]; [n le 8 select I[n] else 1798*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Dec 03 2013

Crossrefs

Cf. A042737, A040868.

Sequence in context: A042732 A042734 A041419 * A042737 A042738 A157498

Adjacent sequences: A042733 A042734 A042735 * A042737 A042738 A042739

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 03 2013

Status

approved