OFFSET
0,5
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
D. N. Lehmer, On ternary continued fractions (Annotated scanned copy)
D. N. Lehmer, On ternary continued fractions, Tohoku Math. J., 37 (1933), 436-445.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Index entries for linear recurrences with constant coefficients, signature (0,7,0,-3,0,1).
FORMULA
G.f.: (-2x^5 + 5x^4 + x^3 - 7x^2 + 1)/(-x^6 + 3x^4 - 7x^2 + 1).
MAPLE
A000962:=(z+1)*(2*z**4-7*z**3+6*z**2+z-1)/(-1+7*z**2-3*z**4+z**6); # conjectured by Simon Plouffe in his 1992 dissertation
a:= n-> (Matrix([[5, 2, 1, 0, 0, 1]]). Matrix(6, (i, j)-> if (i=j-1) then 1 elif j=1 then [0, 7, 0, -3, 0, 1][i] else 0 fi)^n)[1, 6]: seq(a(n), n=0..35); # Alois P. Heinz, Aug 26 2008
MATHEMATICA
CoefficientList[Series[(-2x^5+5x^4+x^3-7x^2+1)/(-x^6+3x^4-7x^2+1), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 10 2012 *)
LinearRecurrence[{0, 7, 0, -3, 0, 1}, {1, 0, 0, 1, 2, 5}, 40] (* Harvey P. Dale, Jun 28 2020 *)
PROG
(PARI) Vec((-2*x^5+5*x^4+x^3-7*x^2+1)/(-x^6+3*x^4-7*x^2+1)+O(x^99)) \\ Charles R Greathouse IV, Apr 10 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved