OFFSET
4,2
COMMENTS
The complete sequence by R. K. Guy in "Anyone for Twopins?" starts with a(0) = 0, a(1) = 1, a(2) = 1 and a(3) = 1. The formula for a(n) confirms these values. - Johannes W. Meijer, Aug 24 2013
REFERENCES
R. K. Guy, ``Anyone for Twopins?,'' in D. A. Klarner, editor, The Mathematical Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 2-15.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. K. Guy, Anyone for Twopins?, in D. A. Klarner, editor, The Mathematical Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 2-15. [Annotated scanned copy, with permission]
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
FORMULA
G.f.: (-x^4*(x^7+x^6+x^5+2*x^4-x^3+x^2-1))/((x^4+x^2-1)*(x^2-x+1)*(x^2+x-1)). - Conjectured by Simon Plouffe in his 1992 dissertation.
a(n) = sum(A102541(n-1, 2*k), k=0..floor((n-1)/2)), n >= 4. - Johannes W. Meijer, Aug 24 2013
a(n) = (1/4) * (2*F(floor((n+1)/2)) + F(n) + A010892(n-1))), with F(n) = A000045(n) the Fibonacci numbers. - Ralf Stephan, from Plouffe's g.f. Aug 25 2013
MAPLE
A005685 := -(-1-z**3+2*z**4+z**2+z**5+z**6+z**7)/(z**2-z+1)/(z**2+z-1)/(z**4+z**2-1);
PROG
(PARI) a(n)=(2*fibonacci(floor((n+1)/2))+fibonacci(n)+[0, 1, 1, 0, -1, -1][(n%6)+1])/4; /* Ralf Stephan, Aug 25 2013 */
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Johannes W. Meijer, Aug 24 2013
STATUS
approved