A014227 Minimal number of initial pieces needed to reach level n in the Solitaire Army game on a hexagonal lattice (a finite sequence).

1, 2, 3, 5, 9, 17, 36, 145

Offset: 0

Author

N. J. A. Sloane and E. M. Rains

Keywords

• nonn
• fini
• full

Comments

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

Proved finite in 1991 by John Duncan and Donald Hayes, the last term in the sequence being a(7). - George Bell (gibell(AT)comcast.net), Jul 11 2006

References

• E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 715.
• John Duncan and Donald Hayes, Triangular Solitaire, Journal of Recreational Mathematics, Vol. 23, p. 26-37 (1991)

Links

• G. I. Bell, D. S. Hirschberg, and P. Guerrero-Garcia, The minimum size required of a solitaire army, arXiv:math/0612612 [math.CO], 2006-2007.
• G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

Crossrefs

Cf. A014225.

Extensions

a(5) and a(6) from George I. Bell (gibell(AT)comcast.net), Feb 02 2007

On Apr 07 2008, Pablo Guerrero-Garcia reports that he together with George I. Bell and Daniel S. Hirschberg have completed the calculation of a(7) and its value is 145. This took nearly 47 hours of computation with a Pentium 4 (AT) 2.80 GHz, 768Mb RAM machine.