

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



91, 1047, 5453, 18903, 51205, 117585, 239891, 447797, 780007, 1285459, 2024529, 3070235, 4509441, 6444061, 8992263, 12289673, 16490579, 21769135, 28320565, 36362367, 46135517, 57905673, 71964379, 88630269, 108250271, 131200811
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS



LINKS



FORMULA

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


EXAMPLE

Some solutions for n=5:
0 0 0 0 0 0 0 0
3 0 4 4 2 1 5 3 4 2 4 1 1 5 3 3
0 1 2 1 1 4 3 1 2 5 4 0 6 6 5 1 0 4 2 510 8 4 8


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



