A125730 - OEIS

%I #13 Sep 21 2017 03:24:48

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

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

%C Note that the first six terms are Fibonacci numbers.

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

%H M. Aigner, <a href="http://www.jstor.org/stable/2691046">Moving into the desert with Fibonacci</a>, Mathematics Magazine, 70 (1997), 11-21.

%H G. I. Bell, <a href="http://www.gibell.net/pegsolitaire/army/index.html">The peg solitaire army</a>.

%H G. I. Bell, D. S. Hirschberg and P. Guerrero-Garcia, <a href="https://arxiv.org/abs/math/0612612">The minimum size required of a solitaire army</a>, arXiv:math/0612612 [math.CO], 2006-2007.

%H N. Eriksen, H. Eriksson and K. Eriksson, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v7i1r3">Diagonal checker-jumping and Eulerian numbers for color-signed permutations</a>, Electron. J. Combin., 7 (2000), #R3.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConwaysSoldiers.html">Conway's Soldiers</a>.

%F 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.

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

%Y Cf. A014225, A014227.

%K fini,full,nonn

%O 0,2

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