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A243638 Number of length n+2 0..7 arrays with no three unequal elements in a row and new values 0..7 introduced in 0..7 order.

%I A243638 #8 Nov 02 2018 12:28:32
%S A243638 4,9,21,51,127,324,844,2243,6073,16737,46905,133556,386062,1132106,
%T A243638 3365610,10137369,30919271,95444507,298042003,941032182,3002839544,
%U A243638 9679707876,31506186516,103497873819,342976360273,1146003129573
%N A243638 Number of length n+2 0..7 arrays with no three unequal elements in a row and new values 0..7 introduced in 0..7 order.
%H A243638 R. H. Hardin, <a href="/A243638/b243638.txt">Table of n, a(n) for n = 1..210</a>
%F A243638 Empirical: a(n) = 13*a(n-1) - 56*a(n-2) + 44*a(n-3) + 305*a(n-4) - 633*a(n-5) - 476*a(n-6) + 1772*a(n-7) + 308*a(n-8) - 2060*a(n-9) - 368*a(n-10) + 864*a(n-11) + 288*a(n-12).
%F A243638 Empirical g.f.: x*(4 - 43*x + 128*x^2 + 106*x^3 - 976*x^4 + 392*x^5 + 2696*x^6 - 1239*x^7 - 3714*x^8 + 363*x^9 + 2016*x^10 + 576*x^11) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)*(1 - 2*x - 2*x^2)*(1 - 2*x - 4*x^2)*(1 - 2*x - 6*x^2)). - _Colin Barker_, Nov 02 2018
%e A243638 Some solutions for n=6:
%e A243638 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A243638 ..0....0....0....0....1....0....0....1....1....1....1....0....1....0....1....0
%e A243638 ..1....1....0....1....1....1....1....1....1....1....1....1....1....1....1....1
%e A243638 ..0....0....1....1....0....1....1....2....1....0....0....0....2....0....2....0
%e A243638 ..1....1....0....1....0....2....1....2....2....0....0....0....2....0....2....1
%e A243638 ..0....1....1....1....1....1....0....0....2....1....2....1....2....0....0....0
%e A243638 ..0....1....1....2....0....1....1....0....3....0....0....1....2....0....2....0
%e A243638 ..0....0....1....1....1....1....0....3....3....0....0....2....2....0....0....1
%Y A243638 Column 7 of A243641.
%K A243638 nonn
%O A243638 1,1
%A A243638 _R. H. Hardin_, Jun 08 2014