A042042 Numerators of continued fraction convergents to sqrt(545).

23, 47, 70, 607, 677, 1961, 90883, 183727, 274610, 2380607, 2655217, 7691041, 356443103, 720577247, 1077020350, 9336740047, 10413760397, 30164260841, 1397969759083, 2826103779007, 4224073538090

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, 3922, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (23 +47*x +70*x^2 +607*x^3 +677*x^4 +1961*x^5 +677*x^6 -607*x^7 +70*x^8 -47*x^9 +23*x^10 -x^11) / (1 -3922*x^6 +x^12). - Vincenzo Librandi, Nov 13 2013

a(n) = 3922*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 14 2013

Mathematica

Numerator[Convergents[Sqrt[545], 30]] (* Harvey P. Dale, Oct 28 2012 *)
CoefficientList[Series[(23 + 47 x + 70 x^2 + 607 x^3 + 677 x^4 + 1961 x^5 + 677 x^6 - 607 x^7 + 70 x^8 - 47 x^9 + 23 x^10 - x^11)/(1 - 3922 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 13 2013 *)

Prog

(Magma) I:=[23, 47, 70, 607, 677, 1961, 90883, 183727, 274610, 2380607, 2655217, 7691041]; [n le 12 select I[n] else 3922*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 14 2013

Crossrefs

Cf. A042043.

Sequence in context: A244092 A042046 A042044 * A130063 A183010 A134517

Adjacent sequences: A042039 A042040 A042041 * A042043 A042044 A042045

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved