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%I #4 Nov 11 2014 08:01:29
%S 21,735,21,7224,1299,21,40320,18966,2292,21,160545,142170,50028,4030,
%T 21,509691,715155,505154,132054,7054,21,1375080,2753061,3213429,
%U 1800040,348066,12284,21,3281544,8746524,15002490,14492075,6415638,915064,21276
%N T(n,k)=Number of length n+6 0..k arrays with no seven consecutive terms having the maximum of any two terms equal to the minimum of the remaining five terms
%C Table starts
%C .21....735.....7224......40320.......160545........509691........1375080
%C .21...1299....18966.....142170.......715155.......2753061........8746524
%C .21...2292....50028.....505154......3213429......15002490.......56118016
%C .21...4030...132054....1800040.....14492075......82072086......361440380
%C .21...7054...348066....6415638.....65419155.....449532868.....2330996068
%C .21..12284...915064...22838540....295152625....2461761504....15032948568
%C .21..21276..2398187...81138873...1329866076...13468748489....96884873906
%C .21..36654..6264519..287576973...5981519744...73595233759...623803084898
%C .21..65647.16780283.1035133361..27178700296..404992490768..4037252105050
%C .21.117118.44934437.3726902703.123528843942.2229198191613.26134202969838
%H R. H. Hardin, <a href="/A250059/b250059.txt">Table of n, a(n) for n = 1..507</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: [linear recurrence of order 98]
%F Empirical for row n:
%F n=1: a(n) = n^7 + (7/2)*n^6 + 7*n^5 + (35/4)*n^4 + (7/2)*n^3 - (7/4)*n^2 - n
%F n=2: [polynomial of degree 8]
%F n=3: [polynomial of degree 9]
%F n=4: [polynomial of degree 10]
%F n=5: [polynomial of degree 11]
%F n=6: [polynomial of degree 12]
%F n=7: [polynomial of degree 13]
%e Some solutions for n=3 k=4
%e ..1....1....1....0....1....1....0....0....1....1....0....0....0....0....0....1
%e ..0....0....0....0....0....1....0....4....3....0....2....4....2....4....1....1
%e ..1....2....0....3....4....4....3....0....1....2....4....0....0....0....1....4
%e ..2....3....3....4....3....2....4....3....4....3....4....4....3....2....2....3
%e ..1....0....1....1....2....4....4....1....0....2....4....3....1....3....0....2
%e ..4....1....2....3....3....2....3....3....2....2....1....2....2....4....1....3
%e ..0....4....2....2....3....3....1....3....0....2....3....4....2....4....1....2
%e ..4....4....2....3....0....0....4....2....2....0....4....3....4....4....0....0
%e ..0....4....2....1....0....0....2....3....4....1....4....0....3....4....4....1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 11 2014