OFFSET
0,1
COMMENTS
With a(-1) = 1, a(n-1) gives, for n >= 0, the denominator of the convergents to 1/sqrt(40) = 1/(2*sqrt(10)). - Wolfdieter Lang, Nov 21 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..100
Index entries for linear recurrences with constant coefficients, signature (0,38,0,-1).
FORMULA
G.f.: -(x+2)*(x^2-8*x-3) / ((x^2-6*x-1)*(x^2+6*x-1)). - Colin Barker, Nov 04 2013
MATHEMATICA
Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[40], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 21 2011*)
Numerator[Convergents[Sqrt[40], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
LinearRecurrence[{0, 38, 0, -1}, {6, 19, 234, 721}, 20] (* Harvey P. Dale, Jul 20 2024 *)
CROSSREFS
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved