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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. 1

%I

%S 91,1047,5453,18903,51205,117585,239891,447797,780007,1285459,2024529,

%T 3070235,4509441,6444061,8992263,12289673,16490579,21769135,28320565,

%U 36362367,46135517,57905673,71964379,88630269,108250271,131200811

%N 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 Row 3 of A195220.

%H R. H. Hardin, <a href="/A195221/b195221.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = (301/30)*n^5 + (301/12)*n^4 + (88/3)*n^3 + (227/12)*n^2 + (199/30)*n + 1.

%F 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 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 Some solutions for n=5:

%e 0 0 0 0 0 0 0 0

%e 3 0 4 4 2 1 -5 -3 -4 -2 -4 -1 -1 -5 3 3

%e 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 Cf. A195220.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 13 2011

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Last modified March 31 07:39 EDT 2023. Contains 361645 sequences. (Running on oeis4.)