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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.

%I A261867 #22 Jun 16 2016 23:28:08
%S A261867 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 A261867 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 A261867 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 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.
%H A261867 Arthur Cayley, <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN600494829_0015&amp;PHYSID=PHYS_0016">On the game of Mousetrap</a>, Quarterly Journal of Pure and Applied Mathematics 15 (1878), pp. 8-10.
%H A261867 Adolph Steen, <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN600494829_0015&amp;PHYSID=PHYS_0238">Some formulas respecting the game of Mousetrap</a>, Quarterly Journal of Pure and Applied Mathematics 15 (1878), pp. 230-241.
%e A261867 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 A261867 Triangle starts with
%e A261867 1
%e A261867 1, 2
%e A261867 1, 3, 2
%e A261867 1, 2, 4, 3
%e A261867 1, 2, 5, 3, 4
%e A261867 ...
%Y A261867 Cf. A007709, A028305.
%K A261867 nonn,tabl
%O A261867 1,3
%A A261867 _Martin Renner_, Sep 03 2015