%I
%S 171,2125,11319,39609,107811,248261,507375,948209,1653019,2725821,
%T 4294951,6515625,9572499,13682229,19096031,26102241,35028875,46246189,
%U 60169239,77260441,98032131,123049125,152931279,188356049,230061051
%N Number of lower triangles of a 3 X 3 integer array with each element differing from all of its vertical and horizontal neighbors by n or less and triangles differing by a constant counted only once.
%C Row 3 of A195278.
%H R. H. Hardin, <a href="/A195279/b195279.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = (64/3)*n^5 + (160/3)*n^4 + 56*n^3 + (92/3)*n^2 + (26/3)*n + 1.
%F Conjectures from _Colin Barker_, Mar 01 2018: (Start)
%F G.f.: x*(171 + 1099*x + 1134*x^2 + 150*x^3 + 7*x^4  x^5) / (1  x)^6.
%F a(n) = 6*a(n1)  15*a(n2) + 20*a(n3)  15*a(n4) + 6*a(n5)  a(n6) for n>6.
%F (End)
%e Some solutions for n=5:
%e ...0.........0.........0.........0.........0.........0.........0.........0
%e ..2.1......3..4.....3..1.....4.1.....1..4.....5.1......5..8......4..4
%e ..3.6.6...2..1..1..7.3..0..5.4.6..4.1..3..7.2..2...8..5..2...0..0.2
%Y Cf. A195278.
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 14 2011
