%I #4 Nov 11 2014 12:35:00

%S 49,444,83,2086,982,144,6835,5604,2228,252,17871,21405,15472,5084,442,

%T 40054,63611,68863,42936,11519,774,80284,159278,232096,222329,117828,

%U 25659,1348,147861,352192,647122,847708,706561,315376,55647,2361,254845

%N T(n,k)=Number of length n+5 0..k arrays with every six consecutive terms having the maximum of some two terms equal to the minimum of the remaining four terms

%C Table starts

%C ...49....444.....2086......6835......17871......40054.......80284.......147861

%C ...83....982.....5604.....21405......63611.....159278......352192.......708609

%C ..144...2228....15472.....68863.....232096.....647122.....1572320......3441309

%C ..252...5084....42936....222329.....847708....2623376.....6978064.....16547001

%C ..442..11519...117828....706561....3032302...10361063....30011560.....76692849

%C ..774..25659...315376...2170435...10384566...38804209...121263104....330977421

%C .1348..55647...813208...6341373...33356124..134387611...446774000...1284748281

%C .2361.122851..2167600..19472847..114688781..508067629..1834111512...5674570869

%C .4156.273803..5855140..60813057..402127048.1962422803..7701187928..25647629649

%C .7334.612178.15883864.190846823.1416804566.7613922448.32463331040.116297027805

%H R. H. Hardin, <a href="/A250081/b250081.txt">Table of n, a(n) for n = 1..2710</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 26]

%F k=2: [order 96]

%F Empirical for row n:

%F n=1: a(n) = 3*n^5 + 10*n^4 + 15*n^3 + (27/2)*n^2 + (13/2)*n + 1

%F n=2: [polynomial of degree 6]

%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=3 k=4

%e ..3....3....3....1....4....4....0....0....3....3....2....0....2....3....3....3

%e ..1....1....1....2....4....3....2....4....3....1....4....3....4....2....0....0

%e ..0....3....2....2....0....3....0....2....3....2....1....2....0....1....0....4

%e ..3....2....3....2....2....0....0....4....2....2....1....3....0....1....2....1

%e ..0....2....3....2....0....0....2....2....1....1....2....2....3....1....3....3

%e ..0....2....2....3....0....0....0....4....2....0....0....3....0....1....0....1

%e ..3....3....3....0....2....1....2....2....4....1....4....2....0....4....0....1

%e ..3....4....1....3....2....4....0....4....2....1....2....3....4....3....1....4

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 11 2014