%I #11 Oct 07 2019 01:58:44
%S 2277,176471,3395245,31640829,189677411,845613769,3048698613,
%T 9369900047,25430520379,62478288201,141479051231,299315365855,
%U 597820942629,1136532061199,2070203713171,3632319367413,6166018879097,10164079181491
%N 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 Row 4 of A195220.
%H R. H. Hardin, <a href="/A195222/b195222.txt">Table of n, a(n) for n = 1..194</a>
%F 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 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 Some solutions for n=5:
%e 0 0 0 0 0 0
%e 5 2 4 5 0 3 5 2 4 4 1 4
%e 2 6 1 0 3 2 5 0 5 3 0 3 5 2 1 3 1 2
%e 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 Cf. A195220.
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 13 2011
