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%I #4 Jun 05 2014 20:37:30
%S 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,
%T 25,65,65,9,2,3,5,10,25,76,187,129,10,2,3,5,10,25,77,263,552,257,11,2,
%U 3,5,10,25,77,279,978,1646,513,12,2,3,5,10,25,77,280,1134,3773,4927,1025,13
%N 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
%C Table starts
%C .2..3....3.....3.....3......3......3......3......3......3......3......3......3
%C .2..4....5.....5.....5......5......5......5......5......5......5......5......5
%C .2..5....9....10....10.....10.....10.....10.....10.....10.....10.....10.....10
%C .2..6...17....24....25.....25.....25.....25.....25.....25.....25.....25.....25
%C .2..7...33....65....76.....77.....77.....77.....77.....77.....77.....77.....77
%C .2..8...65...187...263....279....280....280....280....280....280....280....280
%C .2..9..129...552...978...1134...1156...1157...1157...1157...1157...1157...1157
%C .2.10..257..1646..3773...4979...5267...5296...5297...5297...5297...5297...5297
%C .2.11..513..4927.14824..22981..25915..26406..26443..26444..26444..26444..26444
%C .2.12.1025.14769.58771.109453.135214.141585.142372.142418.142419.142419.142419
%H R. H. Hardin, <a href="/A243519/b243519.txt">Table of n, a(n) for n = 1..9999</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 2*a(n-1) -a(n-2)
%F k=3: a(n) = 3*a(n-1) -2*a(n-2)
%F k=4: a(n) = 5*a(n-1) -7*a(n-2) +3*a(n-3)
%F k=5: a(n) = 8*a(n-1) -21*a(n-2) +22*a(n-3) -8*a(n-4)
%F k=6: a(n) = 12*a(n-1) -52*a(n-2) +102*a(n-3) -91*a(n-4) +30*a(n-5)
%F 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)
%F 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)
%F 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)
%e All solutions for n=3 k=4
%e ..0....0....0....0....0....0....0....0....0....0
%e ..1....1....0....1....0....0....1....0....0....1
%e ..2....2....0....2....1....1....2....0....0....2
%e ..3....0....0....3....2....2....3....1....0....0
%e ..4....1....0....0....0....3....1....2....1....3
%Y Column 3 is A000051
%Y Diagonal is A005001(n+1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jun 05 2014
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