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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

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

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Last modified January 30 19:02 EST 2023. Contains 359947 sequences. (Running on oeis4.)