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A042106 Numerators of continued fraction convergents to sqrt(578). 2
24, 577, 27720, 665857, 31988856, 768398401, 36915112104, 886731088897, 42600007379160, 1023286908188737, 49160371600438536, 1180872205318713601, 56731026226898691384, 1362725501650887306817, 65467555105469489418600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,1154,0,-1).

FORMULA

G.f.: -(x^3 - 24*x^2 - 577*x - 24)/(x^4 - 1154*x^2 + 1). - Vincenzo Librandi, Nov 16 2013

a(n) = 1154*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 16 2013

MATHEMATICA

Numerator[Convergents[Sqrt[578], 30]] (* or *) CoefficientList[Series[-(x^3 - 24 x^2 - 577 x - 24)/(x^4 - 1154 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)

LinearRecurrence[{0, 1154, 0, -1}, {24, 577, 27720, 665857}, 20] (* Harvey P. Dale, Jul 04 2015 *)

PROG

(MAGMA) I:=[24, 577, 27720, 665857]; [n le 4 select I[n] else 1154*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013

CROSSREFS

Cf. A042107.

Sequence in context: A268027 A009968 A041265 * A158637 A179059 A334281

Adjacent sequences:  A042103 A042104 A042105 * A042107 A042108 A042109

KEYWORD

nonn,cofr,frac,easy,less

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified January 27 13:38 EST 2022. Contains 350607 sequences. (Running on oeis4.)