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A242320 Number of length n+5+2 0..5 arrays with every value 0..5 appearing at least once in every consecutive 5+3 elements, and new values 0..5 introduced in order.

%I A242320 #6 Jun 26 2022 19:54:22
%S A242320 266,896,2801,8231,23486,66366,187671,533801,1530356,4371836,12472691,
%T A242320 35574971,101483076,289556006,826266561,2357781941,6727551746,
%U A242320 19195784876,54771887681,156283330211,445932182766,1272403116946
%N A242320 Number of length n+5+2 0..5 arrays with every value 0..5 appearing at least once in every consecutive 5+3 elements, and new values 0..5 introduced in order.
%C A242320 Column 5 of A242322.
%H A242320 R. H. Hardin, <a href="/A242320/b242320.txt">Table of n, a(n) for n = 1..210</a>
%F A242320 Empirical: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) +7*a(n-4) +13*a(n-5) +22*a(n-6) +28*a(n-7) -4*a(n-8) -6*a(n-9) -6*a(n-10) -4*a(n-12) -10*a(n-13) -10*a(n-14) +a(n-16) +a(n-17) +a(n-20) +a(n-21).
%e A242320 Some solutions for n=5
%e A242320 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A242320 ..1....1....1....0....1....1....1....1....1....0....1....1....0....1....1....1
%e A242320 ..0....2....2....0....2....2....2....0....2....1....2....0....1....2....1....1
%e A242320 ..2....3....3....1....3....3....3....2....3....2....0....2....1....3....2....2
%e A242320 ..3....0....1....2....4....4....1....3....0....2....3....3....2....4....3....3
%e A242320 ..4....4....4....3....0....1....4....3....4....3....4....4....3....5....4....1
%e A242320 ..5....4....5....4....5....0....5....4....5....4....4....1....4....3....5....4
%e A242320 ..1....5....2....5....1....5....0....5....2....5....5....5....5....0....0....5
%e A242320 ..3....1....0....2....2....2....3....1....3....4....1....0....0....1....2....0
%e A242320 ..3....0....2....1....0....3....2....3....1....0....2....1....1....4....1....3
%e A242320 ..0....2....3....0....3....1....3....0....3....1....0....4....4....2....1....3
%e A242320 ..2....3....5....2....1....0....3....2....5....1....0....2....2....1....0....2
%Y A242320 Cf. A242322.
%K A242320 nonn
%O A242320 1,1
%A A242320 _R. H. Hardin_, May 10 2014