A005684 Number of Twopins positions. (Formerly M1019)

1, 2, 4, 6, 11, 18, 32, 52, 88, 142, 236, 382, 629, 1018, 1664, 2692, 4383, 7092, 11520, 18640, 30232, 48916, 79264, 128252, 207705, 336074, 544084

Offset

6,2

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

Table of n, a(n) for n=6..32.

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

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,3,-2,0,0,-1).

Formula

G.f.: x^6/( (x^2+x-1)*(x^2-x+1)*(x^4+x^2-1) ). - Ralf Stephan, Apr 21 2004

Maple

A005684:=1/(z**2-z+1)/(z**2+z-1)/(z**4+z**2-1); [Simon Plouffe in his 1992 dissertation.]

Crossrefs

Sequence in context: A328669 A185192 A007053 * A260697 A018167 A295831

Adjacent sequences: A005681 A005682 A005683 * A005685 A005686 A005687

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved