OFFSET
0,1
COMMENTS
From Johannes W. Meijer, Jun 12 2010: (Start)
The terms of this sequence can be constructed with the terms of sequence A087130.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,140,0,0,0,0,1).
FORMULA
a(5*n) = A087130(3*n+1), a(5*n+1) = (A087130(3*n+2) - A087130(3*n+1))/2, a(5*n+2) = ( A087130(3*n+2) + A087130(3*n+1))/2, a(5*n+3) = A087130(3*n+2) and a(5*n+4) = A087130(3*n+3)/2. - Johannes W. Meijer, Jun 12 2010
G.f.: (5 + 11*x + 16*x^2 + 27*x^3 + 70*x^4 + 27*x^5 - 16*x^6 + 11*x^7 - 5*x^8 + x^9)/(1 - 140*x^5 - x^10) - Peter J. C. Moses, Jul 29 2013
MATHEMATICA
Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[29], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011 *)
Numerator[Convergents[Sqrt[29], 30]] (* Vincenzo Librandi, Oct 28 2013 *)
LinearRecurrence[ {0, 0, 0, 0, 140, 0, 0, 0, 0, 1}, {5, 11, 16, 27, 70, 727, 1524, 2251, 3775, 9801}, 30] (* Harvey P. Dale, Jun 10 2021 *)
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved