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

Author

R. H. Hardin, Nov 04 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A246473

Row 1 is A059722(n+1)

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