A249707 T(n,k)=Number of length n+3 0..k arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms

10, 39, 14, 100, 69, 20, 205, 208, 125, 28, 366, 485, 440, 221, 38, 595, 966, 1153, 896, 377, 52, 904, 1729, 2524, 2601, 1724, 659, 72, 1305, 2864, 4893, 6172, 5425, 3440, 1177, 100, 1810, 4473, 8688, 12789, 13666, 11925, 7056, 2119, 138, 2431, 6670, 14433

Offset

1,1

Comments

Table starts

..10...39...100....205.....366.....595.....904.....1305.....1810.....2431

..14...69...208....485.....966....1729....2864.....4473.....6670.....9581

..20..125...440...1153....2524....4893....8688....14433....22756....34397

..28..221...896...2601....6172...12789...24032....41937....69052...108493

..38..377..1724...5425...13666...29673...57912...104289...176350...283481

..52..659..3440..11925...32500...75495..156416...297321...528340...889339

..72.1177..7056..27113...80360..200489..442144...888465..1659976..2924889

.100.2119.14544..61725..198164..528755.1235840..2613945..5113060..9391327

.138.3805.29620.137593..474302.1341901.3295784..7275729.14775346.28054653

.190.6857.60416.307437.1140694.3434085.8902160.20616873.43717054.86348977

Links

R. H. Hardin, Table of n, a(n) for n = 1..8549

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-4)

k=2: [order 10]

k=3: [order 17]

k=4: [order 24]

k=5: [order 30]

k=6: [order 37]

k=7: [order 43]

Empirical for row n:

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

n=2: a(n) = (1/2)*n^4 + 4*n^3 + (11/2)*n^2 + 3*n + 1

n=3: a(n) = (1/15)*n^5 + 2*n^4 + 7*n^3 + 7*n^2 + (44/15)*n + 1

n=4: a(n) = (7/15)*n^5 + 5*n^4 + 11*n^3 + 8*n^2 + (38/15)*n + 1

n=5: a(n) = (5/3)*n^5 + 10*n^4 + 16*n^3 + 8*n^2 + (4/3)*n + 1

n=6: a(n) = (1/5)*n^6 + (73/15)*n^5 + 18*n^4 + 22*n^3 + (34/5)*n^2 - (13/15)*n + 1

n=7: a(n) = (1/70)*n^7 + (19/15)*n^6 + (178/15)*n^5 + 30*n^4 + (851/30)*n^3 + (56/15)*n^2 - (446/105)*n + 1

Example

Some solutions for n=6 k=4
..3....3....2....4....1....4....3....4....3....1....0....3....3....2....3....2
..1....3....4....1....4....2....3....1....4....1....2....0....3....1....3....1
..0....3....0....1....1....0....2....1....3....2....2....0....3....1....4....2
..1....2....2....1....1....2....4....1....0....1....3....0....4....0....0....4
..1....4....2....4....0....4....3....2....3....1....2....0....2....1....3....2
..1....3....2....1....3....2....3....1....3....1....1....0....3....3....3....1
..0....3....0....1....1....1....3....1....3....3....2....0....3....1....4....2
..4....3....4....1....1....2....2....1....1....1....3....0....4....1....3....4
..1....0....2....0....0....2....3....4....4....0....2....1....1....0....2....2

Crossrefs

Column 1 is A246473

Row 1 is A059722(n+1)

Sequence in context: A218081 A219823 A216591 * A228140 A156674 A360669

Adjacent sequences: A249704 A249705 A249706 * A249708 A249709 A249710

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 04 2014

Status

approved