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%I #8 May 23 2018 15:13:46
%S 4,10,20,35,56,83,116,155,200,251,308,371,440,515,596,683,776,875,980,
%T 1091,1208,1331,1460,1595,1736,1883,2036,2195,2360,2531,2708,2891,
%U 3080,3275,3476,3683,3896,4115,4340,4571,4808,5051,5300,5555,5816,6083,6356
%N Number of n X 1 0..4 arrays with rows and columns lexicographically nondecreasing and no element equal to the number of horizontal and vertical neighbors equal to itself.
%C Column 1 of A201729.
%H R. H. Hardin, <a href="/A201722/b201722.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*n^2 - 6*n + 11 for n>2.
%F Conjectures from _Colin Barker_, May 23 2018: (Start)
%F G.f.: x*(4 - 2*x + 2*x^2 + x^3 + x^4) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.
%F (End)
%e Some solutions for n=8.
%e ..0....3....1....0....0....0....0....1....0....0....0....0....0....0....0....0
%e ..0....3....3....0....0....0....0....3....0....0....0....0....0....0....0....0
%e ..0....3....3....0....0....0....0....3....0....2....0....2....0....0....0....0
%e ..1....3....3....0....0....4....1....3....0....3....0....3....1....1....0....3
%e ..2....4....3....0....2....4....2....4....0....3....2....4....4....2....4....4
%e ..4....4....3....2....3....4....3....4....3....3....3....4....4....2....4....4
%e ..4....4....4....2....3....4....3....4....4....3....3....4....4....3....4....4
%e ..4....4....4....3....3....4....4....4....4....3....4....4....4....3....4....4
%Y Cf. A201729.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 04 2011
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