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A042088 Numerators of continued fraction convergents to sqrt(568). 2
23, 24, 119, 143, 6697, 6840, 34057, 40897, 1915319, 1956216, 9740183, 11696399, 547774537, 559470936, 2785658281, 3345129217, 156661602263, 160006731480, 796688528183, 956695259663, 44804670472681 (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 (0,0,0,286,0,0,0,-1).

FORMULA

G.f.: -(x^7 - 23*x^6 + 24*x^5 - 119*x^4 - 143*x^3 - 119*x^2 - 24*x - 23)/(x^8 - 286*x^4 + 1). - Vincenzo Librandi, Nov 16 2013

a(n) = 286*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 16 2013

MATHEMATICA

Numerator[Convergents[Sqrt[568], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 119 x^4 - 143 x^3 - 119 x^2 - 24 x - 23)/(x^8 - 286 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)

PROG

(MAGMA) I:=[23, 24, 119, 143, 6697, 6840, 34057, 40897]; [n le 8 select I[n] else 286*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013

CROSSREFS

Cf. A042089.

Sequence in context: A214510 A042084 A042082 * A042086 A042090 A042092

Adjacent sequences:  A042085 A042086 A042087 * A042089 A042090 A042091

KEYWORD

nonn,cofr,frac,easy,less

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 18 20:07 EDT 2019. Contains 328197 sequences. (Running on oeis4.)