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A042092 Numerators of continued fraction convergents to sqrt(570). 2
23, 24, 167, 191, 8953, 9144, 63817, 72961, 3420023, 3492984, 24377927, 27870911, 1306439833, 1334310744, 9312304297, 10646615041, 499056596183, 509703211224, 3557275863527, 4066979074751 (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 (0,0,0,382,0,0,0,-1).

FORMULA

G.f.: -(x^7 - 23*x^6 + 24*x^5 - 167*x^4 - 191*x^3 - 167*x^2 - 24*x - 23)/(x^8 - 382*x^4 + 1). - Vincenzo Librandi, Nov 16 2013

a(n) = 382*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 16 2013

MATHEMATICA

Numerator[Convergents[Sqrt[570], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 167 x^4 - 191 x^3 - 167 x^2 - 24 x - 23)/(x^8 - 382 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)

PROG

(MAGMA) I:=[23, 24, 167, 191, 8953, 9144, 63817, 72961]; [n le 8 select I[n] else 382*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013

CROSSREFS

Cf. A042093.

Sequence in context: A042088 A042086 A042090 * A042094 A042096 A042098

Adjacent sequences:  A042089 A042090 A042091 * A042093 A042094 A042095

KEYWORD

nonn,cofr,frac,easy,less

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 21 10:00 EDT 2019. Contains 321368 sequences. (Running on oeis4.)