%I #22 Jun 16 2016 23:28:08
%S 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,
%T 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,
%U 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
%N 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.
%H Arthur Cayley, <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN600494829_0015&PHYSID=PHYS_0016">On the game of Mousetrap</a>, Quarterly Journal of Pure and Applied Mathematics 15 (1878), pp. 8-10.
%H Adolph Steen, <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN600494829_0015&PHYSID=PHYS_0238">Some formulas respecting the game of Mousetrap</a>, Quarterly Journal of Pure and Applied Mathematics 15 (1878), pp. 230-241.
%e 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.
%e Triangle starts with
%e 1
%e 1, 2
%e 1, 3, 2
%e 1, 2, 4, 3
%e 1, 2, 5, 3, 4
%e ...
%Y Cf. A007709, A028305.
%K nonn,tabl
%O 1,3
%A _Martin Renner_, Sep 03 2015