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A195235 Number of lower triangles of a 5 X 5 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

%I A195235 #12 May 06 2018 12:18:45
%S A195235 32768,127785,237818,348849,459880,570911,681942,792973,904004,
%T A195235 1015035,1126066,1237097,1348128,1459159,1570190,1681221,1792252,
%U A195235 1903283,2014314,2125345,2236376,2347407,2458438,2569469,2680500,2791531,2902562,3013593
%N A195235 Number of lower triangles of a 5 X 5 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.
%C A195235 Row 5 of A195232.
%H A195235 R. H. Hardin, <a href="/A195235/b195235.txt">Table of n, a(n) for n = 1..200</a>
%F A195235 Empirical: a(n) = 111031*n - 95275 for n>2.
%F A195235 Conjectures from _Colin Barker_, May 06 2018: (Start)
%F A195235 G.f.: x*(32768 + 62249*x + 15016*x^2 + 998*x^3) / (1 - x)^2.
%F A195235 a(n) = 2*a(n-1) - a(n-2) for n>4.
%F A195235 (End)
%e A195235 Some solutions for n=4 with 0 and 4:
%e A195235 ..0..........4..........4..........0..........4..........0..........0
%e A195235 ..1.1........3.3........3.3........1.1........4.3........1.1........1.1
%e A195235 ..2.2.2......2.2.2......2.2.2......1.2.2......3.3.2......2.2.2......2.2.2
%e A195235 ..3.2.3.3....1.2.2.1....1.2.1.1....1.2.3.3....2.3.2.1....3.3.3.3....3.3.2.3
%e A195235 ..2.3.2.3.4..1.2.2.1.0..2.1.1.0.1..2.2.3.3.4..3.2.2.1.0..2.3.4.4.4..4.3.3.3.4
%Y A195235 Cf. A195232.
%K A195235 nonn
%O A195235 1,1
%A A195235 _R. H. Hardin_, Sep 13 2011