A125730 Minimal number of initial pieces needed to reach level n in the Solitaire Army game when diagonal jumps are allowed.

1, 2, 3, 5, 8, 13, 23, 46, 123

Offset: 0

Author

George I. Bell (gibell(AT)comcast.net), Feb 02 2007

Keywords

• fini
• full
• nonn

Comments

Note that the first six terms are Fibonacci numbers.

Examples

			a(1)=2 because it takes 2 men to go one step or level forward.
		

References

• E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 715.

Links

• M. Aigner, Moving into the desert with Fibonacci, Mathematics Magazine, 70 (1997), 11-21.
• G. I. Bell, The peg solitaire army.
• 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.
• N. Eriksen, H. Eriksson and K. Eriksson, Diagonal checker-jumping and Eulerian numbers for color-signed permutations, Electron. J. Combin., 7 (2000), #R3.
• Eric Weisstein's World of Mathematics, Conway's Soldiers.

Crossrefs

Cf. A014225, A014227.

Formula

It is easy to show that a(n) >= a(n-1)+a(n-2). However, finding the last 3 terms in this sequence is not easy.