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%I #8 Nov 03 2018 10:32:39
%S 1,1,2,4,9,23,65,199,654,2296,8568,33794,140039,605869,2718531,
%T 12564289,59419764,285878342,1392536354,6842206084,33819153429,
%U 167827213315,835048228437,4162123757579,20768689294634,103709892420388
%N Number of length n 0..4 arrays with new values introduced in order from both ends.
%H R. H. Hardin, <a href="/A245159/b245159.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 17*a(n-1) - 118*a(n-2) + 434*a(n-3) - 913*a(n-4) + 1097*a(n-5) - 696*a(n-6) + 180*a(n-7) for n>8.
%F Conjectures from _Colin Barker_, Nov 03 2018: (Start)
%F G.f.: x*(1 - 16*x + 103*x^2 - 346*x^3 + 656*x^4 - 710*x^5 + 425*x^6 - 124*x^7) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)^2*(1 - 5*x)).
%F a(n) = (-3375 - 525*2^(4+n) - 1300*3^n + 3*5^n + 100*(297+9*2^(2+n) + 2*3^n)*n) / 43200.
%F (End)
%e Some solutions for n=7:
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..0....1....0....1....0....1....0....1....1....0....1....1....0....1....0....0
%e ..0....0....1....1....1....0....1....0....1....1....2....2....1....2....0....1
%e ..1....2....2....2....1....1....0....2....0....2....0....1....1....1....0....0
%e ..1....2....1....2....2....0....2....0....0....1....0....1....0....0....1....0
%e ..0....1....0....1....1....0....1....1....1....1....1....0....1....1....1....1
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%Y Column 4 of A245163.
%K nonn
%O 1,3
%A _R. H. Hardin_, Jul 12 2014
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