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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.
1

%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