A042096 Numerators of continued fraction convergents to sqrt(572).

23, 24, 263, 287, 13465, 13752, 150985, 164737, 7728887, 7893624, 86665127, 94558751, 4436367673, 4530926424, 49745631913, 54276558337, 2546467315415, 2600743873752, 28553906052935, 31154649926687

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, 574, 0, 0, 0, -1).

Formula

G.f.: -(x^7 - 23*x^6 + 24*x^5 - 263*x^4 - 287*x^3 - 263*x^2 - 24*x - 23)/(x^8 - 574*x^4 + 1). - Vincenzo Librandi, Nov 16 2013

a(n) = 574*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 16 2013

Mathematica

Numerator[Convergents[Sqrt[572], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 263 x^4 - 287 x^3 - 263 x^2 - 24 x - 23)/(x^8 - 574 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)

Prog

(Magma) I:=[23, 24, 263, 287, 13465, 13752, 150985, 164737]; [n le 8 select I[n] else 574*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013

Crossrefs

Cf. A042097.

Sequence in context: A042090 A042092 A042094 * A042098 A041263 A042100

Adjacent sequences: A042093 A042094 A042095 * A042097 A042098 A042099

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved