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

1,1

Comments

Row 3 of A195220.

Links

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

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 -5-10   8  4  8

Crossrefs

Cf. A195220.

Sequence in context: A170955 A020316 A221815 * A213559 A120756 A027787

Adjacent sequences: A195218 A195219 A195220 * A195222 A195223 A195224

Keyword

nonn

Author

R. H. Hardin, Sep 13 2011

Status

approved