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A242547 Number of length n+3 0..6 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..6 introduced in 0..6 order.

%I A242547 #6 Jul 23 2025 11:17:26
%S A242547 13,43,166,712,3339,16968,92360,532175,3210136,20066475,128848615,
%T A242547 843831762,5605476437,37615886287,254237240993,1726996739311,
%U A242547 11772647808288,80450209850112,550717024856208,3774443585348691
%N A242547 Number of length n+3 0..6 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..6 introduced in 0..6 order.
%C A242547 Column 6 of A242549
%H A242547 R. H. Hardin, <a href="/A242547/b242547.txt">Table of n, a(n) for n = 1..210</a>
%F A242547 Empirical: a(n) = 16*a(n-1) -95*a(n-2) +326*a(n-3) -998*a(n-4) +2268*a(n-5) -2953*a(n-6) +5002*a(n-7) -877*a(n-8) -8932*a(n-9) -5460*a(n-10) -46536*a(n-11) -36728*a(n-12) -4608*a(n-13) +43488*a(n-14) +180288*a(n-15) +260208*a(n-16) +254016*a(n-17) +207360*a(n-18) +103680*a(n-19) +20736*a(n-20)
%e A242547 Some solutions for n=4
%e A242547 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A242547 ..1....0....1....1....1....1....1....1....0....1....1....1....1....1....0....1
%e A242547 ..1....0....2....0....2....1....2....1....1....2....2....2....1....2....1....0
%e A242547 ..2....1....1....2....3....2....1....0....2....3....0....2....2....0....0....2
%e A242547 ..3....0....3....1....1....3....3....2....1....3....3....1....3....2....0....0
%e A242547 ..1....2....3....1....4....2....0....1....0....0....3....0....0....2....2....3
%e A242547 ..1....1....1....0....1....2....3....3....2....3....4....3....1....3....1....3
%K A242547 nonn
%O A242547 1,1
%A A242547 _R. H. Hardin_, May 17 2014