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

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

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 A339500 A373359

Adjacent sequences: A243516 A243517 A243518 * A243520 A243521 A243522

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 05 2014

Status

approved