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%I #4 Nov 19 2014 07:14:24
%S 44,429,68,2056,907,108,6785,5264,1989,172,17796,20085,14040,4409,272,
%T 39949,59396,62041,37824,9771,424,80144,147903,206724,193437,101264,
%U 21523,648,147681,325312,569693,725596,596245,266448,46941,996,254620
%N T(n,k)=Number of length n+5 0..k arrays with every six consecutive terms having the maximum of some three terms equal to the minimum of the remaining three terms
%C Table starts
%C ...44....429.....2056......6785.....17796......39949.......80144......147681
%C ...68....907.....5264.....20085.....59396.....147903......325312......651369
%C ..108...1989....14040.....62041....206724.....569693.....1369136.....2966769
%C ..172...4409....37824....193437....725596....2210213.....5794496....13561449
%C ..272...9771...101264....596245...2506320....8403783....23943648....60312393
%C ..424..21523...266448...1789193...8357144...30606683....94080768...253309665
%C ..648..46941...682576...5156313..26422104..104374957...341862816...971811153
%C ..996.103647..1775840..15207653..86279700..371391819..1310493568..3979387305
%C .1544.231359..4688592..45754029.288823480.1360791587..5193605728.16905033465
%C .2404.519971.12466400.138814961.976092436.5038261323.20813768640.72664579185
%H R. H. Hardin, <a href="/A250336/b250336.txt">Table of n, a(n) for n = 1..2035</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-3) +2*a(n-6) -2*a(n-9) -a(n-10) -a(n-12) +a(n-15)
%F k=2: [order 70]
%F Empirical for row n:
%F n=1: a(n) = 3*n^5 + 10*n^4 + 15*n^3 + 11*n^2 + 4*n + 1
%F n=2: a(n) = n^6 + 9*n^5 + 20*n^4 + (68/3)*n^3 + 12*n^2 + (7/3)*n + 1
%F n=3: [polynomial of degree 7]
%F n=4: [polynomial of degree 8]
%F n=5: [polynomial of degree 9]
%F n=6: [polynomial of degree 9]
%F n=7: [polynomial of degree 9]
%e Some solutions for n=4 k=4
%e ..0....0....0....2....0....1....0....0....1....0....0....2....0....0....0....0
%e ..3....1....1....0....2....4....4....1....4....4....3....2....1....1....0....1
%e ..4....3....3....0....3....1....1....2....0....2....3....2....2....0....0....4
%e ..3....3....4....2....3....1....2....2....1....2....3....2....4....1....0....1
%e ..3....3....1....2....3....0....2....4....1....1....3....2....2....2....0....1
%e ..2....4....1....4....3....1....2....2....1....2....4....3....2....2....0....0
%e ..4....4....1....4....1....1....2....0....1....4....4....0....1....1....0....0
%e ..1....2....1....0....2....2....4....1....0....1....3....4....3....1....1....3
%e ..3....1....2....0....3....4....2....2....0....3....0....2....0....1....2....1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 19 2014