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%I #4 Jun 06 2013 12:52:39
%S 1,1,2,1,2,4,1,2,6,10,1,2,6,22,32,1,2,6,24,90,122,1,2,6,24,118,422,
%T 544,1,2,6,24,120,658,2226,2770,1,2,6,24,120,718,4078,13102,15872,1,2,
%U 6,24,120,720,4914,27724,85170,101042,1,2,6,24,120,720,5038,37300,205134,606542
%N T(n,k)=Number of permutations of 1..n with fewer than k interior elements having values lying between the values of their neighbors
%C Table starts
%C .......1........1.........1.........1.........1.........1.........1.........1
%C .......2........2.........2.........2.........2.........2.........2.........2
%C .......4........6.........6.........6.........6.........6.........6.........6
%C ......10.......22........24........24........24........24........24........24
%C ......32.......90.......118.......120.......120.......120.......120.......120
%C .....122......422.......658.......718.......720.......720.......720.......720
%C .....544.....2226......4078......4914......5038......5040......5040......5040
%C ....2770....13102.....27724.....37300.....40066.....40318.....40320.....40320
%C ...15872....85170....205134....308460....353556....362370....362878....362880
%C ..101042...606542...1641534...2748354...3399246...3600306...3627778...3628798
%C ..707584..4697946..14132390..26194542..35142546..38963958..39830282..39914754
%C .5405530.39330982.130299584.265691456.387129588.453658380.475089392.478739984
%H R. H. Hardin, <a href="/A226441/b226441.txt">Table of n, a(n) for n = 1..9999</a>
%e Some solutions for n=8 k=4
%e ..5....8....1....7....5....5....8....4....7....5....3....4....7....6....5....1
%e ..8....1....7....3....1....4....1....7....2....4....5....2....2....5....3....2
%e ..6....5....2....6....3....8....7....5....1....3....7....1....5....4....7....7
%e ..7....6....6....8....6....6....6....1....5....8....2....7....1....7....6....4
%e ..3....7....3....2....7....3....3....3....6....1....6....5....8....1....1....3
%e ..4....3....8....1....4....7....2....8....4....7....4....8....3....8....2....6
%e ..1....4....5....5....8....2....5....6....3....6....1....6....4....3....4....8
%e ..2....2....4....4....2....1....4....2....8....2....8....3....6....2....8....5
%Y Column 1 is A001250
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_ Jun 06 2013
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