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A014227
Minimal number of initial pieces needed to reach level n in the Solitaire Army game on a hexagonal lattice (a finite sequence).
3
1, 2, 3, 5, 9, 17, 36, 145
OFFSET
0,2
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.
CROSSREFS
Cf. A014225.
Sequence in context: A110113 A341960 A137155 * A334816 A064769 A320641
KEYWORD
nonn,fini,full
AUTHOR
N. J. A. Sloane and E. M. Rains
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.
STATUS
approved