

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



2277, 176471, 3395245, 31640829, 189677411, 845613769, 3048698613, 9369900047, 25430520379, 62478288201, 141479051231, 299315365855, 597820942629, 1136532061199, 2070203713171, 3632319367413, 6166018879097, 10164079181491
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OFFSET

1,1


COMMENTS



LINKS



FORMULA

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.
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


EXAMPLE

Some solutions for n=5:
0 0 0 0 0 0
5 2 4 5 0 3 5 2 4 4 1 4
2 6 1 0 3 2 5 0 5 3 0 3 5 2 1 3 1 2
3 1 6 1 3 2 5 7 4 4 2 4 3 2 0 1 7 2 6 4 0 2 3 6


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



