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A242548 Number of length n+3 0..7 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..7 introduced in 0..7 order.

%I A242548 #6 Jul 23 2025 11:17:33
%S A242548 13,43,166,712,3340,17004,93103,543773,3362689,21854355,148145552,
%T A242548 1039764960,7504319914,55361803579,415379230159,3156808241415,
%U A242548 24223346602916,187213792659552,1454634743756302,11346966341306231
%N A242548 Number of length n+3 0..7 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..7 introduced in 0..7 order.
%C A242548 Column 7 of A242549
%H A242548 R. H. Hardin, <a href="/A242548/b242548.txt">Table of n, a(n) for n = 1..210</a>
%F A242548 Empirical: a(n) = 22*a(n-1) -190*a(n-2) +924*a(n-3) -3465*a(n-4) +10962*a(n-5) -24402*a(n-6) +45828*a(n-7) -74016*a(n-8) +19016*a(n-9) -23090*a(n-10) -159064*a(n-11) +571211*a(n-12) +704098*a(n-13) +1846562*a(n-14) +2774132*a(n-15) +616507*a(n-16) -2599138*a(n-17) -8906720*a(n-18) -16117180*a(n-19) -18096476*a(n-20) -15823920*a(n-21) -10584000*a(n-22) -4233600*a(n-23) -705600*a(n-24)
%e A242548 Some solutions for n=4
%e A242548 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A242548 ..1....1....1....1....1....1....1....1....0....0....1....1....1....1....1....1
%e A242548 ..1....2....0....2....0....2....2....2....1....1....1....1....0....2....1....2
%e A242548 ..0....2....2....1....0....0....3....3....2....2....2....1....0....3....2....3
%e A242548 ..2....1....2....3....2....0....1....2....1....1....3....0....1....4....0....4
%e A242548 ..1....2....1....4....1....2....0....1....3....0....3....2....2....1....0....4
%e A242548 ..1....3....3....0....2....3....3....1....0....2....2....1....3....0....0....0
%K A242548 nonn
%O A242548 1,1
%A A242548 _R. H. Hardin_, May 17 2014