A249844 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

10, 110, 10, 560, 198, 10, 1920, 1500, 359, 10, 5170, 6916, 4064, 653, 10, 11830, 23526, 25206, 11052, 1189, 10, 24080, 65226, 108250, 92190, 30080, 2163, 10, 44880, 156184, 363349, 499654, 337396, 81816, 3966, 10, 78090, 335016, 1022672, 2029683, 2307418

Offset

1,1

Comments

Table starts

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

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

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

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

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

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

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

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

.10.13311.1668211..60928967.1054123407.11096650996..82120356870..467585930650

.10.24352.4554827.223459265.4875176581.62077669371.539644444522.3531991262078

Links

R. H. Hardin, Table of n, a(n) for n = 1..1549

Formula

Empirical for column k:

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

k=2: [linear recurrence of order 40]

k=3: [order 70]

Empirical for row n:

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

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

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

n=4: [polynomial of degree 8]

n=5: [polynomial of degree 9]

n=6: [polynomial of degree 10]

n=7: [polynomial of degree 11]

Example

Some solutions for n=4 k=4
..0....3....3....2....4....4....3....2....3....4....4....2....1....0....0....3
..3....3....1....0....4....3....2....3....4....2....1....1....2....2....0....1
..4....1....2....2....2....2....4....4....4....1....4....4....2....0....1....1
..1....2....0....1....4....4....3....4....1....4....2....3....3....4....3....0
..2....3....0....0....1....4....0....2....4....3....1....4....0....1....2....0
..3....3....1....2....4....4....1....0....1....4....4....0....0....3....0....3
..3....4....1....2....0....2....0....4....2....1....0....4....3....3....4....4
..1....1....2....0....3....2....1....1....2....0....0....2....3....0....1....1

Crossrefs

Sequence in context: A281044 A281519 A281633 * A105030 A280528 A281278

Adjacent sequences: A249841 A249842 A249843 * A249845 A249846 A249847

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 07 2014

Status

approved