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A041067
Denominators of continued fraction convergents to sqrt(40).
3
1, 3, 37, 114, 1405, 4329, 53353, 164388, 2026009, 6242415, 76934989, 237047382, 2921503573, 9001558101, 110940200785, 341822160456, 4212806126257, 12980240539227, 159975692596981, 492907318330170, 6074863512559021, 18717497856007233, 230684837784645817
OFFSET
0,2
COMMENTS
With a(-1) = 0, a(n-1) gives, for n >= 0, the numerator of the convergents to 1/sqrt(40) = 1/(2*sqrt(10)) = A020797. - Wolfdieter Lang, Nov 21 2017
FORMULA
G.f.: -(x^2-3*x-1) / ((x^2-6*x-1)*(x^2+6*x-1)). - Colin Barker, Nov 12 2013
a(n) = 38*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 10 2013
MATHEMATICA
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[40], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 21 2011 *)
Denominator[Convergents[Sqrt[40], 30]] (* Harvey P. Dale, Sep 12 2013 *)
CoefficientList[Series[-(x^2 - 3 x - 1)/((x^2 - 6 x - 1)(x^2 + 6 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2013 *)
PROG
(Magma) I:=[1, 3, 37, 114]; [n le 4 select I[n] else 38*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 10 2013
CROSSREFS
Cf. A010494, A041066 (numerators).
Sequence in context: A300636 A301358 A163156 * A046867 A154823 A109835
KEYWORD
nonn,cofr,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 12 2013
STATUS
approved