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%I #13 Oct 29 2023 02:21:39
%S 1,1,2,1,3,6,1,3,10,24,1,3,11,40,120,1,3,11,44,182,720,1,3,11,45,192,
%T 938,5040,1,3,11,45,196,892,5424,40320,1,3,11,45,197,898,4400,34788,
%U 362880,1,3,11,45,197,902,4272,23086,244544,3628800,1,3,11,45,197,903,4274,21002,129250,1865144,39916800
%N T(n,k) is the number of n element 1..n arrays with each element the minimum of k adjacent elements of a permutation of 1..n+k-1 of n+k-1 elements.
%H R. H. Hardin, <a href="/A217891/b217891.txt">Table of n, a(n) for n = 1..159</a>
%e Table starts:
%e .........1.........1........1........1........1........1.......1......1......1
%e .........2.........3........3........3........3........3.......3......3......3
%e .........6........10.......11.......11.......11.......11......11.....11.....11
%e ........24........40.......44.......45.......45.......45......45.....45.....45
%e .......120.......182......192......196......197......197.....197....197....197
%e .......720.......938......892......898......902......903.....903....903....903
%e ......5040......5424.....4400.....4272.....4274.....4278....4279...4279...4279
%e .....40320.....34788....23086....21002....20790....20788...20792..20793..20793
%e ....362880....244544...129250...106564...103354...103050..103044.103048.103049
%e ...3628800...1865144...773868...558780...523786...519268..518864.518854
%e ..39916800..15312976..4953208..3037926..2703206..2653278.2647244
%e .479001600.134495328.33778104.17203726.14210824.13725388
%e Some solutions for n=4 and k=4:
%e ..1....2....3....1....2....2....1....1....1....2....1....1....4....2....2....3
%e ..2....4....4....1....4....3....3....3....1....1....1....1....3....2....2....3
%e ..3....1....2....3....3....4....4....2....2....1....3....4....1....1....4....2
%e ..3....1....1....3....1....1....2....2....3....1....4....3....1....1....1....1
%Y Diagonal is A001003.
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_, Oct 14 2012
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