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A243603 Number of length n+2 0..6 arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..6 introduced in 0..6 order.

%I A243603 #6 Jul 23 2025 11:20:56
%S A243603 4,10,29,97,366,1533,7020,34631,181391,995139,5651157,32902123,
%T A243603 194971159,1169639664,7076433285,43062727014,263096669677,
%U A243603 1611790269519,9892521309824,60793268309048,373921041602730,2301237378396793
%N A243603 Number of length n+2 0..6 arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..6 introduced in 0..6 order.
%C A243603 Column 6 of A243607
%H A243603 R. H. Hardin, <a href="/A243603/b243603.txt">Table of n, a(n) for n = 1..210</a>
%F A243603 Empirical: a(n) = 17*a(n-1) -106*a(n-2) +286*a(n-3) -245*a(n-4) -231*a(n-5) +329*a(n-6) +147*a(n-7) -106*a(n-8) -74*a(n-9) -15*a(n-10) -a(n-11)
%e A243603 Some solutions for n=5
%e A243603 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A243603 ..1....1....1....0....1....1....1....1....1....1....1....1....1....0....1....0
%e A243603 ..2....2....2....1....2....2....2....2....1....2....1....2....1....1....2....1
%e A243603 ..2....2....0....2....3....3....2....3....2....2....2....3....1....1....3....1
%e A243603 ..2....0....0....3....0....0....1....1....3....3....0....4....2....2....3....2
%e A243603 ..3....0....3....3....2....4....3....4....3....4....0....4....0....3....4....3
%e A243603 ..3....0....4....4....2....5....3....4....2....0....2....1....1....4....5....1
%K A243603 nonn
%O A243603 1,1
%A A243603 _R. H. Hardin_, Jun 07 2014