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A242471 Number of length n+2 0..8 arrays with no three equal elements in a row and new values 0..8 introduced in 0..8 order.

%I A242471 #6 Jul 23 2025 11:16:46
%S A242471 4,12,41,159,685,3233,16534,90862,532958,3317613,21803646,150528288,
%T A242471 1086089333,8146481406,63182485967,504037166445,4115582321241,
%U A242471 34244236336515,289252828167957,2472398717507023,21329556857593204
%N A242471 Number of length n+2 0..8 arrays with no three equal elements in a row and new values 0..8 introduced in 0..8 order.
%C A242471 Column 8 of A242472
%H A242471 R. H. Hardin, <a href="/A242471/b242471.txt">Table of n, a(n) for n = 1..133</a>
%F A242471 Empirical: a(n) = 29*a(n-1) -314*a(n-2) +1449*a(n-3) -1442*a(n-4) -8855*a(n-5) +16059*a(n-6) +34312*a(n-7) -42104*a(n-8) -101900*a(n-9) -6124*a(n-10) +112608*a(n-11) +106128*a(n-12) +40320*a(n-13) +5760*a(n-14)
%e A242471 Some solutions for n=5
%e A242471 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A242471 ..1....1....1....1....1....1....1....1....1....0....1....1....1....1....1....0
%e A242471 ..2....2....2....1....2....1....2....1....2....1....2....1....1....2....2....1
%e A242471 ..3....3....2....2....2....0....3....2....3....2....3....2....0....3....3....2
%e A242471 ..0....0....3....2....1....2....0....2....4....3....2....2....1....0....4....0
%e A242471 ..4....4....4....0....2....2....2....3....2....4....0....1....1....3....1....3
%e A242471 ..0....5....4....1....1....3....4....3....1....3....4....3....2....1....2....1
%K A242471 nonn
%O A242471 1,1
%A A242471 _R. H. Hardin_, May 15 2014