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A195223 Number of lower triangles of a 5 X 5 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 A195223 #16 Oct 07 2019 03:03:28
%S A195223 111031,92031109,9032683465,289301569283,4677360495205,47764170577925,
%T A195223 350767341744137,2010235691940497,9496465116615081,38429133040711965,
%U A195223 136997589911672127,439401533118090493,1288688520518224397
%N A195223 Number of lower triangles of a 5 X 5 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 A195223 Row 5 of A195220.
%H A195223 R. H. Hardin, <a href="/A195223/b195223.txt">Table of n, a(n) for n = 1..43</a>
%F A195223 Empirical: a(n) = (3508493543/18345600)*n^14 + (3508493543/2620800)*n^13 + (1116775769537/239500800)*n^12 + (422094048023/39916800)*n^11 + (377328209183/21772800)*n^10 + (78475421219/3628800)*n^9 + (1073748492569/50803200)*n^8 + (19848770813/1209600)*n^7 + (221251862417/21772800)*n^6 + (18121075223/3628800)*n^5 + (10435002133/5443200)*n^4 + (505904317/907200)*n^3 + (8793472607/75675600)*n^2 + (1397863/90090)*n + 1.
%F A195223 Since a(n) is an Ehrhart polynomial of degree 14 (see A195220), and the empirical polynomial fits the Data for 1 <= n <= 15, it must be correct. - _Robert Israel_, Oct 06 2019
%e A195223 Some solutions for n=5:
%e A195223   0               0               0               0               0
%e A195223   2  4            5  2            3  3            1  5            1  4
%e A195223   7  2  3         1  5  6         5  7  6         2  3  2        -1  0 -1
%e A195223   5  4  3  7      2  4  1  1      3  8  7  3      5  6  3  0      0  3  0  2
%e A195223   6  5  6  2  5   5  3  6  3  1   5  3  5  6  2   9  7  2  0  0   5  3 -1  4  3
%Y A195223 Cf. A195220.
%K A195223 nonn
%O A195223 1,1
%A A195223 _R. H. Hardin_, Sep 13 2011