OFFSET
0,3
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).
A. Tarn, Approximations to certain square roots and the series of numbers connected therewith, Mathematical Questions and Solutions from the Educational Times, 1 (1916), 8-12.
LINKS
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
R. C. Read, Letter to N. J. A. Sloane, Oct. 29, 1976
Albert Tarn, Approximations to certain square roots and the series of numbers connected therewith [Annotated scanned copy]
Index entries for linear recurrences with constant coefficients, signature (0, 8, 0, -9).
FORMULA
a(n)=8a(n-2)-9a(n-4). - Mario Catalani (mario.catalani(AT)unito.it), Apr 24 2003
G.f.: (1+x-4x^2+3x^3)/(1-8x^2+9x^4). a(n)/A002536(n) converges to sqrt(7). - Mario Catalani (mario.catalani(AT)unito.it), Apr 24 2003
a(n+1) = x^n + (-1)^n*(x-2)^n where x = (1+sqrt(7)) and the term is divided by 2 for a(2) and a(3), 4 for a(4) and a(5)... 2^n for a(2n) and a(2n+1). - Ben Paul Thurston, Aug 30 2006
MAPLE
A002537:=(1+z-4*z**2+3*z**3)/(1-8*z**2+9*z**4); # conjectured by Simon Plouffe in his 1992 dissertation
MATHEMATICA
LinearRecurrence[{0, 8, 0, -9}, {1, 1, 4, 11}, 40] (* Harvey P. Dale, Jul 24 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from James A. Sellers, Sep 08 2000
STATUS
approved