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A195249 Number of lower triangles of a 3 X 3 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by two or less.

%I A195249 #9 May 06 2018 12:18:32
%S A195249 64,729,1682,2729,3776,4823,5870,6917,7964,9011,10058,11105,12152,
%T A195249 13199,14246,15293,16340,17387,18434,19481,20528,21575,22622,23669,
%U A195249 24716,25763,26810,27857,28904,29951,30998,32045,33092,34139,35186,36233,37280,38327
%N A195249 Number of lower triangles of a 3 X 3 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by two or less.
%C A195249 Row 3 of A195248.
%H A195249 R. H. Hardin, <a href="/A195249/b195249.txt">Table of n, a(n) for n = 1..200</a>
%F A195249 Empirical: a(n) = 1047*n - 1459 for n>2.
%F A195249 Conjectures from _Colin Barker_, May 06 2018: (Start)
%F A195249 G.f.: x*(64 + 601*x + 288*x^2 + 94*x^3) / (1 - x)^2.
%F A195249 a(n) = 2*a(n-1) - a(n-2) for n>4.
%F A195249 (End)
%e A195249 Some solutions for n=5:
%e A195249 ..2......1......0......0......4......5......1......1......5......3
%e A195249 ..3.4....2.3....2.0....0.2....5.4....3.5....1.3....2.3....3.3....2.2
%e A195249 ..4.4.4..2.1.2..1.1.1..1.1.3..4.4.5..5.5.3..2.1.3..4.3.4..2.3.3..0.0.2
%Y A195249 Cf. A195248.
%K A195249 nonn
%O A195249 1,1
%A A195249 _R. H. Hardin_, Sep 13 2011