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A243605 Number of length n+2 0..8 arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..8 introduced in 0..8 order.

%I A243605 #6 Jul 23 2025 11:21:10
%S A243605 4,10,29,97,366,1534,7050,35166,188788,1082913,6592698,42315731,
%T A243605 284431573,1988554321,14365186163,106571030511,807548257486,
%U A243605 6221612919342,48551842571129,382621726260959,3037888284516885
%N A243605 Number of length n+2 0..8 arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..8 introduced in 0..8 order.
%C A243605 Column 8 of A243607
%H A243605 R. H. Hardin, <a href="/A243605/b243605.txt">Table of n, a(n) for n = 1..210</a>
%F A243605 Empirical: a(n) = 30*a(n-1) -365*a(n-2) +2297*a(n-3) -7771*a(n-4) +12461*a(n-5) -2366*a(n-6) -15807*a(n-7) +7237*a(n-8) +10936*a(n-9) -841*a(n-10) -3849*a(n-11) -1625*a(n-12) -307*a(n-13) -28*a(n-14) -a(n-15)
%e A243605 Some solutions for n=5
%e A243605 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A243605 ..0....0....0....1....0....1....1....0....1....1....1....1....0....1....0....1
%e A243605 ..1....0....1....1....1....2....2....0....2....2....2....2....1....2....1....1
%e A243605 ..1....1....2....2....1....0....0....1....3....2....3....2....2....3....1....2
%e A243605 ..1....2....3....3....0....1....0....1....1....3....4....1....0....4....1....0
%e A243605 ..2....3....1....4....2....3....3....1....0....4....5....3....0....0....0....1
%e A243605 ..2....0....1....0....3....4....3....2....4....5....6....3....3....0....0....2
%K A243605 nonn
%O A243605 1,1
%A A243605 _R. H. Hardin_, Jun 07 2014