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A195221 Number of lower triangles of a 3 X 3 integer array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by n or less and triangles differing by a constant counted only once.

%I A195221 #16 Oct 07 2019 01:59:02
%S A195221 91,1047,5453,18903,51205,117585,239891,447797,780007,1285459,2024529,
%T A195221 3070235,4509441,6444061,8992263,12289673,16490579,21769135,28320565,
%U A195221 36362367,46135517,57905673,71964379,88630269,108250271,131200811
%N A195221 Number of lower triangles of a 3 X 3 integer array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by n or less and triangles differing by a constant counted only once.
%C A195221 Row 3 of A195220.
%H A195221 R. H. Hardin, <a href="/A195221/b195221.txt">Table of n, a(n) for n = 1..200</a>
%F A195221 Empirical: a(n) = (301/30)*n^5 + (301/12)*n^4 + (88/3)*n^3 + (227/12)*n^2 + (199/30)*n + 1.
%F A195221 Empirical g.f.: x*(91 + 501*x + 536*x^2 + 70*x^3 + 7*x^4 - x^5) / (1 - x)^6. - _Colin Barker_, May 06 2018
%F A195221 Since a(n) is an Ehrhart polynomial of degree 5 (see A195220), and the empirical polynomial fits the Data for 1 <= n <= 6, it must be correct. - _Robert Israel_, Oct 06 2019
%e A195221 Some solutions for n=5:
%e A195221   0         0         0         0         0         0         0         0
%e A195221   3  0      4  4      2  1     -5 -3     -4 -2     -4 -1     -1 -5      3  3
%e A195221   0 -1 -2  -1 -1  4  -3  1 -2  -5 -4  0  -6 -6 -5   1  0 -4  -2 -5-10   8  4  8
%Y A195221 Cf. A195220.
%K A195221 nonn
%O A195221 1,1
%A A195221 _R. H. Hardin_, Sep 13 2011