A005690 Number of Twopins positions. (Formerly M0999)

1, 2, 4, 6, 9, 12, 18, 26, 41, 62, 96, 142, 212, 308, 454, 662, 979, 1438, 2128, 3126, 4606, 6748, 9910, 14510, 21298, 31212, 45820, 67176, 98571, 144476

Offset

8,2

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=8..37.

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^8]/[(x^3-x+1)(x^3+x-1)(x^6+x^2-1)]. - Ralf Stephan, Apr 22 2004

Maple

A005690:=1/(z**3+z-1)/(z**3-z+1)/(z**6+z**2-1); [Conjectured (correctly) by Simon Plouffe in his 1992 dissertation.]

Crossrefs

Sequence in context: A267161 A173784 A094660 * A364378 A005779 A351075

Adjacent sequences: A005687 A005688 A005689 * A005691 A005692 A005693

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved