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A243519 T(n,k)=Number of length n+2 0..k arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..k introduced in 0..k order 7
2, 3, 2, 3, 4, 2, 3, 5, 5, 2, 3, 5, 9, 6, 2, 3, 5, 10, 17, 7, 2, 3, 5, 10, 24, 33, 8, 2, 3, 5, 10, 25, 65, 65, 9, 2, 3, 5, 10, 25, 76, 187, 129, 10, 2, 3, 5, 10, 25, 77, 263, 552, 257, 11, 2, 3, 5, 10, 25, 77, 279, 978, 1646, 513, 12, 2, 3, 5, 10, 25, 77, 280, 1134, 3773, 4927, 1025, 13 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

.2..3....3.....3.....3......3......3......3......3......3......3......3......3

.2..4....5.....5.....5......5......5......5......5......5......5......5......5

.2..5....9....10....10.....10.....10.....10.....10.....10.....10.....10.....10

.2..6...17....24....25.....25.....25.....25.....25.....25.....25.....25.....25

.2..7...33....65....76.....77.....77.....77.....77.....77.....77.....77.....77

.2..8...65...187...263....279....280....280....280....280....280....280....280

.2..9..129...552...978...1134...1156...1157...1157...1157...1157...1157...1157

.2.10..257..1646..3773...4979...5267...5296...5297...5297...5297...5297...5297

.2.11..513..4927.14824..22981..25915..26406..26443..26444..26444..26444..26444

.2.12.1025.14769.58771.109453.135214.141585.142372.142418.142419.142419.142419

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..9999

FORMULA

Empirical for column k:

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

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

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

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

k=5: a(n) = 8*a(n-1) -21*a(n-2) +22*a(n-3) -8*a(n-4)

k=6: a(n) = 12*a(n-1) -52*a(n-2) +102*a(n-3) -91*a(n-4) +30*a(n-5)

k=7: a(n) = 17*a(n-1) -111*a(n-2) +355*a(n-3) -584*a(n-4) +468*a(n-5) -144*a(n-6)

k=8: a(n) = 23*a(n-1) -212*a(n-2) +1010*a(n-3) -2669*a(n-4) +3887*a(n-5) -2878*a(n-6) +840*a(n-7)

k=9: a(n) = 30*a(n-1) -372*a(n-2) +2478*a(n-3) -9639*a(n-4) +22260*a(n-5) -29588*a(n-6) +20592*a(n-7) -5760*a(n-8)

EXAMPLE

All solutions for n=3 k=4

..0....0....0....0....0....0....0....0....0....0

..1....1....0....1....0....0....1....0....0....1

..2....2....0....2....1....1....2....0....0....2

..3....0....0....3....2....2....3....1....0....0

..4....1....0....0....0....3....1....2....1....3

CROSSREFS

Column 3 is A000051

Diagonal is A005001(n+1)

Sequence in context: A097352 A076050 A130799 * A278102 A106383 A175794

Adjacent sequences:  A243516 A243517 A243518 * A243520 A243521 A243522

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 05 2014

STATUS

approved

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Last modified October 15 11:03 EDT 2018. Contains 316224 sequences. (Running on oeis4.)