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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 8
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 (list; table; graph; refs; listen; history; text; internal format)
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 A145009 A090229

Adjacent sequences:  A243041 A243042 A243043 * A243045 A243046 A243047

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 29 2014

STATUS

approved

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Last modified October 22 16:15 EDT 2021. Contains 348174 sequences. (Running on oeis4.)