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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 A339500 A106383 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 July 30 07:41 EDT 2021. Contains 346348 sequences. (Running on oeis4.)