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

0,2

Comments

Note that the first six terms are Fibonacci numbers.

References

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

Links

Table of n, a(n) for n=0..8.

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.

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.

Example

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

Crossrefs

Cf. A014225, A014227.

Sequence in context: A096796 A257418 A370001 * A340708 A074030 A336604

Adjacent sequences: A125727 A125728 A125729 * A125731 A125732 A125733

Keyword

fini,full,nonn

Author

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

Status

approved