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A195222 Number of lower triangles of a 4 X 4 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 A195222 #11 Oct 07 2019 01:58:44
%S A195222 2277,176471,3395245,31640829,189677411,845613769,3048698613,
%T A195222 9369900047,25430520379,62478288201,141479051231,299315365855,
%U A195222 597820942629,1136532061199,2070203713171,3632319367413,6166018879097,10164079181491
%N A195222 Number of lower triangles of a 4 X 4 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 A195222 Row 4 of A195220.
%H A195222 R. H. Hardin, <a href="/A195222/b195222.txt">Table of n, a(n) for n = 1..194</a>
%F A195222 Empirical: a(n) = (1207573/30240)*n^9 + (1207573/6720)*n^8 + (1000157/2520)*n^7 + (264247/480)*n^6 + (754417/1440)*n^5 + (338651/960)*n^4 + (2533393/15120)*n^3 + (90763/1680)*n^2 + (901/84)*n + 1.
%F A195222 Since a(n) is an Ehrhart polynomial of degree 9 (see A195220), and the empirical polynomial fits the Data for 1 <= n <= 10, it must be correct. - _Robert Israel_, Oct 06 2019
%e A195222 Some solutions for n=5:
%e A195222    0            0            0            0            0            0
%e A195222   -5 -2         4  5         0  3         5  2        -4 -4         1 -4
%e A195222   -2 -6 -1      0  3  2      5  0  5      3  0 -3     -5 -2 -1     -3  1 -2
%e A195222   -3 -1 -6 -1   3  2  5  7   4  4  2  4   3  2  0  1  -7 -2 -6 -4   0 -2 -3 -6
%Y A195222 Cf. A195220.
%K A195222 nonn
%O A195222 1,1
%A A195222 _R. H. Hardin_, Sep 13 2011