

A014227


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


3




OFFSET

0,2


COMMENTS

The hexagonal lattice is the familiar 2dimensional 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. 2637 (1991)


LINKS

Table of n, a(n) for n=0..7.
G. I. Bell, D. S. Hirschberg, P. GuerreroGarcia, The minimum size required of a solitaire army.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2


CROSSREFS

Cf. A014225.
Sequence in context: A179807 A110113 A137155 * A064769 A320641 A047021
Adjacent sequences: A014224 A014225 A014226 * A014228 A014229 A014230


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 GuerreroGarcia 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



