A261867 Triangle T(n, k) read by rows (n >= 1, 1 <= k <= n), where row n gives the lexicographically first permutation of n cards that is a winning (or reformed) deck at Cayley's Mousetrap.

1, 1, 2, 1, 3, 2, 1, 2, 4, 3, 1, 2, 5, 3, 4, 1, 2, 4, 3, 6, 5, 1, 2, 3, 7, 6, 5, 4, 1, 2, 3, 5, 8, 4, 6, 7, 1, 2, 3, 4, 8, 5, 7, 9, 6, 1, 2, 3, 4, 6, 9, 8, 7, 10, 5, 1, 2, 3, 4, 6, 7, 5, 11, 8, 10, 9, 1, 2, 3, 4, 5, 8, 10, 6, 12, 9, 11, 7, 1, 2, 3, 4, 5, 6, 9, 12, 7, 10, 13, 11, 8, 1, 2, 3, 4, 5, 6, 10, 9, 14, 13, 8, 11, 12, 7, 1, 2, 3, 4, 5, 6, 8, 9, 12, 7, 14, 10, 15, 13, 11

Offset: 1

Author

Martin Renner, Sep 03 2015

Keywords

• nonn
• tabl

Examples

			With four cards in the order 1243 the player will win the first time (out of six times), taking the cards away in the order 1342, i.e., the cards held in hand develop from 1243 -> 243 -> 24 -> 2.
Triangle starts with
1
1, 2
1, 3, 2
1, 2, 4, 3
1, 2, 5, 3, 4
...
		

Links

• Arthur Cayley, On the game of Mousetrap, Quarterly Journal of Pure and Applied Mathematics 15 (1878), pp. 8-10.
• Adolph Steen, Some formulas respecting the game of Mousetrap, Quarterly Journal of Pure and Applied Mathematics 15 (1878), pp. 230-241.

Crossrefs

Cf. A007709, A028305.