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A242319 Number of length n+4+2 0..4 arrays with every value 0..4 appearing at least once in every consecutive 4+3 elements, and new values 0..4 introduced in order.

%I A242319 #6 Jul 23 2025 11:16:10
%S A242319 140,440,1300,3648,10012,27368,75236,208976,577964,1596216,4408020,
%T A242319 12176768,33645500,92967176,256849892,709617776,1960543660,5416680632,
%U A242319 14965468916,41347189280,114235439996,315613828040,871989852740
%N A242319 Number of length n+4+2 0..4 arrays with every value 0..4 appearing at least once in every consecutive 4+3 elements, and new values 0..4 introduced in order.
%C A242319 Column 4 of A242322
%H A242319 R. H. Hardin, <a href="/A242319/b242319.txt">Table of n, a(n) for n = 1..210</a>
%F A242319 Empirical: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) +6*a(n-4) +10*a(n-5) +12*a(n-6) -4*a(n-7) -6*a(n-8) -6*a(n-9) -2*a(n-11) -2*a(n-12) +a(n-14) +a(n-15)
%e A242319 Some solutions for n=5
%e A242319 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A242319 ..1....1....1....1....1....1....1....0....1....1....1....0....0....1....1....1
%e A242319 ..0....2....2....2....0....0....1....1....2....2....2....1....1....0....2....2
%e A242319 ..2....1....2....3....2....2....2....2....3....2....0....2....2....2....0....0
%e A242319 ..3....3....3....3....3....3....3....2....1....3....3....1....0....3....3....3
%e A242319 ..2....0....4....0....4....0....4....3....4....4....4....3....3....2....4....1
%e A242319 ..4....4....1....4....0....4....0....4....0....1....1....4....4....4....1....4
%e A242319 ..3....1....0....2....0....1....2....0....3....0....0....2....1....1....2....0
%e A242319 ..1....2....2....1....1....2....1....1....2....1....2....0....2....0....0....0
%e A242319 ..0....2....0....4....2....0....2....2....1....2....3....4....2....0....1....2
%e A242319 ..3....1....4....4....0....3....4....3....1....4....0....1....4....4....4....3
%K A242319 nonn
%O A242319 1,1
%A A242319 _R. H. Hardin_, May 10 2014