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%I #4 May 29 2014 10:31:03
%S 6,12,9,13,32,13,13,42,85,19,13,43,147,226,28,13,43,162,536,601,41,13,
%T 43,163,672,1987,1598,60,13,43,163,693,2962,7414,4249,88,13,43,163,
%U 694,3223,13540,27736,11298,129,13,43,163,694,3251,16060,63221,103868,30041,189
%N T(n,k)=Number of length n+3 0..k arrays with no four elements in a row with pattern abba (possibly a=b) and new values 0..k introduced in 0..k order
%C Table starts
%C ...6....12......13......13.......13.......13.......13.......13.......13
%C ...9....32......42......43.......43.......43.......43.......43.......43
%C ..13....85.....147.....162......163......163......163......163......163
%C ..19...226.....536.....672......693......694......694......694......694
%C ..28...601....1987....2962.....3223.....3251.....3252.....3252.....3252
%C ..41..1598....7414...13540....16060....16516....16552....16553....16553
%C ..60..4249...27736...63221....84207....89891....90634....90679....90680
%C ..88.11298..103868..298775...457676...517995...529587...530734...530789
%C .129.30041..389129.1421589..2549156..3124633..3276946..3298816..3300512
%C .189.79878.1458054.6789700.14430921.19526936.21309360.21657357.21696132
%H R. H. Hardin, <a href="/A243033/b243033.txt">Table of n, a(n) for n = 1..6280</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-3)
%F k=2: a(n) = 2*a(n-1) +a(n-2) +2*a(n-3)
%F k=3: a(n) = 4*a(n-1) -a(n-2) +2*a(n-3) -6*a(n-4) -2*a(n-5) -3*a(n-6)
%F k=4: [order 9]
%F k=5: [order 12]
%F k=6: [order 15]
%F k=7: [order 18]
%e Some solutions for n=3 k=4
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..1....0....1....1....1....1....0....1....0....0....1....0....1....1....0....1
%e ..2....0....2....1....0....2....0....2....1....1....2....1....1....2....1....0
%e ..0....1....1....1....0....0....1....0....2....0....0....1....2....1....2....2
%e ..2....0....1....0....2....3....0....0....1....2....2....2....2....2....2....1
%e ..1....1....0....1....3....0....2....3....1....0....0....1....2....3....3....3
%Y Column 1 is A000930(n+5)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, May 29 2014
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