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A243640 Number of length n+2 0..9 arrays with no three unequal elements in a row and new values 0..9 introduced in 0..9 order.

%I A243640 #6 Jul 23 2025 11:21:30
%S A243640 4,9,21,51,127,324,844,2243,6073,16737,46905,133556,386062,1132107,
%T A243640 3365627,10137559,30920943,95457177,298128257,941574130,3006037464,
%U A243640 9697650031,31602766791,104000078093,345512414521,1158493006765
%N A243640 Number of length n+2 0..9 arrays with no three unequal elements in a row and new values 0..9 introduced in 0..9 order.
%C A243640 Column 9 of A243641
%H A243640 R. H. Hardin, <a href="/A243640/b243640.txt">Table of n, a(n) for n = 1..210</a>
%F A243640 Empirical: a(n) = 17*a(n-1) -99*a(n-2) +125*a(n-3) +931*a(n-4) -3185*a(n-5) -1785*a(n-6) +19063*a(n-7) -6754*a(n-8) -56936*a(n-9) +32132*a(n-10) +99764*a(n-11) -41096*a(n-12) -100896*a(n-13) +5152*a(n-14) +42048*a(n-15) +11520*a(n-16)
%e A243640 Some solutions for n=5
%e A243640 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A243640 ..1....0....0....1....1....1....0....0....1....0....0....0....0....1....1....1
%e A243640 ..0....1....1....1....0....1....0....1....0....1....0....0....1....0....1....0
%e A243640 ..1....0....1....1....1....2....0....1....0....0....1....1....0....0....1....0
%e A243640 ..1....0....1....1....0....1....0....2....2....0....0....0....0....0....0....0
%e A243640 ..1....1....2....0....0....1....0....2....2....0....0....1....2....0....1....0
%e A243640 ..2....1....2....1....1....3....1....0....2....2....2....0....0....1....1....0
%K A243640 nonn
%O A243640 1,1
%A A243640 _R. H. Hardin_, Jun 08 2014