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A245158 Number of length n 0..3 arrays with new values introduced in order from both ends.

%I A245158 #11 Nov 03 2018 10:32:27
%S A245158 1,1,2,4,9,23,65,199,653,2275,8313,31439,121637,477307,1888721,
%T A245158 7509799,29940861,119550419,477742889,1909988479,7637856725,
%U A245158 30546970411,122178444417,488693854679,1954733475629,7818845822083,31275198738905
%N A245158 Number of length n 0..3 arrays with new values introduced in order from both ends.
%H A245158 R. H. Hardin, <a href="/A245158/b245158.txt">Table of n, a(n) for n = 1..210</a>
%F A245158 Empirical: a(n) = 10*a(n-1) - 37*a(n-2) + 64*a(n-3) - 52*a(n-4) + 16*a(n-5) for n>6.
%F A245158 Conjectures from _Colin Barker_, Nov 03 2018: (Start)
%F A245158 G.f.: x*(1 - 9*x + 29*x^2 - 43*x^3 + 31*x^4 - 11*x^5) / ((1 - x)^2*(1 - 2*x)^2*(1 - 4*x)).
%F A245158 a(n) = (-64 - 27*2^(2+n) + 4^n + 12*(32+3*2^n)*n) / 576 for n>1.
%F A245158 (End)
%e A245158 Some solutions for n=7:
%e A245158 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A245158 ..0....0....1....0....1....1....1....1....1....1....1....0....0....1....1....1
%e A245158 ..0....0....0....1....1....2....0....2....2....0....0....1....0....0....1....2
%e A245158 ..0....1....0....1....0....0....1....2....1....2....2....0....0....0....2....1
%e A245158 ..1....2....0....2....1....2....1....1....0....1....1....1....0....0....0....1
%e A245158 ..0....1....0....1....0....1....0....0....0....1....0....0....0....1....1....0
%e A245158 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%Y A245158 Column 3 of A245163.
%K A245158 nonn
%O A245158 1,3
%A A245158 _R. H. Hardin_, Jul 12 2014