The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000963 The convergent sequence B_n for the ternary continued fraction (3,1;2,2) of period 2. (Formerly M2660 N1062) 2
 0, 1, 0, 3, 7, 16, 49, 104, 322, 683, 2114, 4485, 13881, 29450, 91147, 193378, 598500, 1269781, 3929940, 8337783, 25805227, 54748516, 169445269, 359496044, 1112631142 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 REFERENCES D. N. Lehmer, On ternary continued fractions, Tohoku Math. J., 37 (1933), 436-445. 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) Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992 FORMULA G.f.: (-2x^5 + 7x^4 - 4x^3 + x)/(-x^6 + 3x^4 - 7x^2 + 1). MAPLE A000963:=z*(-1+4*z**2-7*z**3+2*z**4)/(-1+7*z**2-3*z**4+z**6); # conjectured by Simon Plouffe in his 1992 dissertation a:= n-> (Matrix([[16, 7, 3, 0, 1, 0]]). 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..24); # Alois P. Heinz, Aug 26 2008 MATHEMATICA CoefficientList[Series[(-2x^5+7x^4-4x^3+x)/(-x^6+3x^4-7x^2+1), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 11 2012 *) CROSSREFS Cf. A000962, A000964. Sequence in context: A341576 A143817 A297210 * A133593 A297154 A305348 Adjacent sequences:  A000960 A000961 A000962 * A000964 A000965 A000966 KEYWORD nonn,cofr,easy AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 11 00:03 EDT 2021. Contains 342877 sequences. (Running on oeis4.)