A243044 T(n,k)=Number of length n+3 0..k arrays with no four elements in a row with pattern abab (with a!=b) and new values 0..k introduced in 0..k order

7, 13, 13, 14, 36, 24, 14, 46, 101, 44, 14, 47, 163, 285, 81, 14, 47, 178, 602, 806, 149, 14, 47, 179, 738, 2271, 2281, 274, 14, 47, 179, 759, 3255, 8655, 6457, 504, 14, 47, 179, 760, 3516, 14932, 33148, 18280, 927, 14, 47, 179, 760, 3544, 17463, 70167, 127255, 51753

Offset

1,1

Comments

Table starts

....7.....13......14......14.......14.......14.......14.......14.......14

...13.....36......46......47.......47.......47.......47.......47.......47

...24....101.....163.....178......179......179......179......179......179

...44....285.....602.....738......759......760......760......760......760

...81....806....2271....3255.....3516.....3544.....3545.....3545.....3545

..149...2281....8655...14932....17463....17919....17955....17956....17956

..274...6457...33148...70167....91409....97106....97849....97894....97895

..504..18280..127255..334488...496910...557629...569236...570383...570438

..927..51753..489084.1608035..2773138..3355754..3508656..3530543..3532239

.1705.146521.1880732.7768793.15753844.20947076.22742717.23091543.23130337

Links

R. H. Hardin, Table of n, a(n) for n = 1..6281

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2) +a(n-3)

k=2: a(n) = 3*a(n-1) -a(n-3) -a(n-4)

k=3: a(n) = 5*a(n-1) -3*a(n-2) -5*a(n-3) -3*a(n-4) +3*a(n-5) +3*a(n-6) +a(n-7)

k=4: [order 10]

k=5: [order 13]

k=6: [order 16]

k=7: [order 19]

Example

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

Crossrefs

Column 1 is A000073(n+5)

Sequence in context: A243389 A242584 A135555 * A229831 A372206 A372083

Adjacent sequences: A243041 A243042 A243043 * A243045 A243046 A243047

Keyword

nonn,tabl

Author

R. H. Hardin, May 29 2014

Status

approved