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A267228 Number of length-n 0..4 arrays with no following elements greater than or equal to the first repeated value.

%I A267228 #8 Feb 05 2018 17:08:12
%S A267228 5,25,110,470,1980,8274,34396,142474,588596,2426738,9989292,41065818,
%T A267228 168636772,691859842,2836150748,11617837802,47559474708,194575978386,
%U A267228 795613053964,3251559375226,13282278193604,54232112235170
%N A267228 Number of length-n 0..4 arrays with no following elements greater than or equal to the first repeated value.
%C A267228 Column 4 of A267232.
%H A267228 R. H. Hardin, <a href="/A267228/b267228.txt">Table of n, a(n) for n = 1..210</a>
%F A267228 Empirical: a(n) = 14*a(n-1) -75*a(n-2) +190*a(n-3) -224*a(n-4) +96*a(n-5) for n>6.
%F A267228 Conjectures from _Colin Barker_, Feb 05 2018: (Start)
%F A267228 G.f.: x*(5 - 45*x + 135*x^2 - 145*x^3 + 20*x^4 + 24*x^5) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)^2).
%F A267228 a(n) = (2*(-3*2^(1+n) - 8*3^n + 41*4^n - 8) + 3*4^n*n) / 48 for n>1.
%F A267228 (End)
%e A267228 Some solutions for n=6:
%e A267228 ..1....0....0....4....0....4....1....2....2....0....1....1....2....3....1....3
%e A267228 ..4....4....3....2....1....4....2....3....0....2....3....4....0....1....3....1
%e A267228 ..3....2....2....3....0....0....0....2....1....2....2....1....3....4....0....2
%e A267228 ..0....4....3....1....4....3....1....0....2....1....1....3....4....0....2....3
%e A267228 ..4....0....2....0....2....3....4....4....4....0....3....1....2....3....0....0
%e A267228 ..2....2....2....0....1....0....0....3....1....0....1....3....3....3....3....4
%Y A267228 Cf. A267232.
%K A267228 nonn
%O A267228 1,1
%A A267228 _R. H. Hardin_, Jan 12 2016