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.

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

Offset: 1

Author

R. H. Hardin, Sep 13 2011

Keywords

• nonn

Comments

Row 3 of A195220.

Examples

			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 -5-10   8  4  8
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A195220.

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