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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. 1

%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

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Last modified September 16 19:55 EDT 2024. Contains 375977 sequences. (Running on oeis4.)