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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. 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
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.
EXAMPLE
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
...
CROSSREFS
Sequence in context: A114905 A200651 A126597 * A076081 A304089 A209281
KEYWORD
nonn,tabl
AUTHOR
Martin Renner, Sep 03 2015
STATUS
approved

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Last modified July 23 10:25 EDT 2024. Contains 374547 sequences. (Running on oeis4.)