%I #4 Nov 07 2014 07:47:34

%S 10,110,10,560,198,10,1920,1500,359,10,5170,6916,4064,653,10,11830,

%T 23526,25206,11052,1189,10,24080,65226,108250,92190,30080,2163,10,

%U 44880,156184,363349,499654,337396,81816,3966,10,78090,335016,1022672,2029683,2307418

%N T(n,k)=Number of length n+4 0..k arrays with no five consecutive terms having the maximum of any two terms equal to the minimum of the remaining three terms

%C Table starts

%C .10...110.....560......1920.......5170.......11830........24080.........44880

%C .10...198....1500......6916......23526.......65226.......156184........335016

%C .10...359....4064.....25206.....108250......363349......1022672.......2522796

%C .10...653...11052.....92190.....499654.....2029683......6712760......19039308

%C .10..1189...30080....337396....2307418....11342301.....44075760.....143723664

%C .10..2163...81816...1234328...10653298....63374127....289372688....1084868616

%C .10..3966..223505...4527441...49270055...354521087...1901506446....8194431990

%C .10..7269..610707..16609691..227902341..1983461964..12496226122...61900389630

%C .10.13311.1668211..60928967.1054123407.11096650996..82120356870..467585930650

%C .10.24352.4554827.223459265.4875176581.62077669371.539644444522.3531991262078

%H R. H. Hardin, <a href="/A249844/b249844.txt">Table of n, a(n) for n = 1..1549</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

%F k=2: [linear recurrence of order 40]

%F k=3: [order 70]

%F Empirical for row n:

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

%F n=2: a(n) = n^6 + (9/5)*n^5 + 3*n^4 + 3*n^3 + n^2 + (1/5)*n

%F n=3: a(n) = n^7 + (6/5)*n^6 + 3*n^5 + 3*n^4 + (5/6)*n^3 + (4/5)*n^2 + (1/6)*n

%F n=4: [polynomial of degree 8]

%F n=5: [polynomial of degree 9]

%F n=6: [polynomial of degree 10]

%F n=7: [polynomial of degree 11]

%e Some solutions for n=4 k=4

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

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

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 07 2014