A042044 Numerators of continued fraction convergents to sqrt(546).

23, 47, 70, 187, 257, 701, 32503, 65707, 98210, 262127, 360337, 982801, 45569183, 92121167, 137690350, 367501867, 505192217, 1377886301, 63887962063, 129153810427, 193041772490, 515237355407, 708279127897

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1402,0,0,0,0,0,-1).

Formula

G.f.: -(x^11 - 23*x^10 + 47*x^9 - 70*x^8 + 187*x^7 -257*x^6 - 701*x^5 - 257*x^4 - 187*x^3 - 70*x^2 - 47*x - 23)/(x^12 - 1402*x^6 + 1). - Vincenzo Librandi, Nov 13 2013

a(n) = 1402*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 14 2013

Mathematica

Numerator[Convergents[Sqrt[546], 30]] (* or *) CoefficientList[Series[-(x^11 - 23 x^10 + 47 x^9 - 70 x^8 + 187 x^7 - 257 x^6 - 701 x^5 - 257 x^4 - 187 x^3 - 70 x^2 - 47 x - 23)/(x^12 - 1402 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 14 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 1402, 0, 0, 0, 0, 0, -1}, {23, 47, 70, 187, 257, 701, 32503, 65707, 98210, 262127, 360337, 982801}, 30] (* Harvey P. Dale, Jun 29 2021 *)

Prog

(Magma) I:=[23, 47, 70, 187, 257, 701, 32503, 65707, 98210, 262127, 360337, 982801]; [n le 12 select I[n] else 1402*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 14 2013

Crossrefs

Cf. A042045.

Sequence in context: A201019 A244092 A042046 * A042042 A130063 A183010

Adjacent sequences: A042041 A042042 A042043 * A042045 A042046 A042047

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved