A125730 - OEIS

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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 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,2`
	COMMENTS	`Note that the first six terms are Fibonacci numbers.`
	REFERENCES	`M. Aigner, Moving into the desert with Fibonacci, Mathematics Magazine, 70 (1997), 11-21.` `E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 715.` `N. Eriksen, H. Eriksson and K. Eriksson, Diagonal checker-jumping and Eulerian numbers for colorsigned permutations, Electron. J. Combin., 7 (2000), #R3.`
	LINKS	`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.` `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: A018067 A068202 A096796 * A074030 A024318 A132915` `Adjacent sequences: A125727 A125728 A125729 * A125731 A125732 A125733`
	KEYWORD	`fini,full,nonn`
	AUTHOR	`George I. Bell (gibell(AT)comcast.net), Feb 02 2007`

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Last modified February 17 08:44 EST 2012. Contains 205998 sequences.