OFFSET
0,1
COMMENTS
The terms of this sequence can be constructed with the terms of sequence A086902. For the terms of the periodical sequence of the continued fraction for sqrt(53) see A010139. We observe that its period is five. The decimal expansion of sqrt(53) is A010506. - Johannes W. Meijer, Jun 12 2010
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,364,0,0,0,0,1).
FORMULA
a(5*n) = A086902(3*n+1), a(5*n+1) = (A086902(3*n+2)-A086902(3*n+1))/2, a(5*n+2) = (A086902(3*n+2)+A086902(3*n+1))/2, a(5*n+3) = A086902(3*n+2) and a(5*n+4) = A086902(3*n+3)/2. - Johannes W. Meijer, Jun 12 2010
G.f.: -(x^9-7*x^8+22*x^7-29*x^6+51*x^5+182*x^4+51*x^3+29*x^2+22*x+7) / (x^10+364*x^5-1). - Colin Barker, Sep 26 2013
MATHEMATICA
Numerator[Convergents[Sqrt[53], 30]] (* Harvey P. Dale, Sep 24 2013 *)
CoefficientList[Series[-(x^9 - 7 x^8 + 22 x^7 - 29 x^6 + 51 x^5 + 182 x^4 + 51 x^3 + 29 x^2 + 22 x + 7)/(x^10 + 364 x^5 - 1), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 27 2013 *)
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Sep 26 2013
STATUS
approved