A250014 T(n,k)=Number of length n+5 0..k arrays with no six consecutive terms having the maximum of any three terms equal to the minimum of the remaining three terms

20, 300, 20, 2040, 520, 20, 8840, 5200, 912, 20, 28860, 30360, 13512, 1612, 20, 77700, 125780, 106352, 35440, 2864, 20, 182000, 412160, 558588, 375756, 93384, 5102, 20, 383760, 1140160, 2224848, 2499284, 1332504, 246560, 9090, 20, 745380, 2776080

Offset

1,1

Comments

Table starts

.20...300.....2040......8840.......28860........77700........182000

.20...520.....5200.....30360......125780.......412160.......1140160

.20...912....13512....106352......558588......2224848.......7259024

.20..1612....35440....375756.....2499284.....12088256......46481536

.20..2864....93384...1332504....11215276.....65834856.....298220320

.20..5102...246560...4732480....50383892....358850926....1914587120

.20..9090...651144..16813550...226419876...1956551556...12294501768

.20.16272..1723328..59817840..1018508340..10675467072...78993574080

.20.29158..4564240.212915478..4583261868..58265451392..507664903912

.20.52262.12092304.758003332.20627283972.318035896726.3262820072464

Links

R. H. Hardin, Table of n, a(n) for n = 1..640

Formula

Empirical for column k:

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

k=2: [linear recurrence of order 55]

Empirical for row n:

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

n=2: a(n) = n^7 + 2*n^6 + 4*n^5 + 5*n^4 + (17/3)*n^3 + 3*n^2 - (2/3)*n

n=3: [polynomial of degree 8]

n=4: [polynomial of degree 9]

n=5: [polynomial of degree 10]

n=6: [polynomial of degree 11]

n=7: [polynomial of degree 12]

Example

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

Crossrefs

Sequence in context: A001708 A016255 A322052 * A291256 A250015 A344197

Adjacent sequences: A250011 A250012 A250013 * A250015 A250016 A250017

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 10 2014

Status

approved