A195279 Number of lower triangles of a 3 X 3 integer array with each element differing from all of its vertical and horizontal neighbors by n or less and triangles differing by a constant counted only once.

171, 2125, 11319, 39609, 107811, 248261, 507375, 948209, 1653019, 2725821, 4294951, 6515625, 9572499, 13682229, 19096031, 26102241, 35028875, 46246189, 60169239, 77260441, 98032131, 123049125, 152931279, 188356049, 230061051

Offset: 1

Author

R. H. Hardin, Sep 14 2011

Keywords

• nonn

Comments

Row 3 of A195278.

Examples

			Some solutions for n=5:
...0.........0.........0.........0.........0.........0.........0.........0
..-2.-1......3..4.....-3..1.....-4.-1.....-1..4.....-5.-1......5..8......4..4
..-3.-6.-6...2..1..1..-7.-3..0..-5.-4.-6..-4.-1..3..-7.-2..2...8..5..2...0..0.-2
		

Links

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

Crossrefs

Cf. A195278.

Formula

Empirical: a(n) = (64/3)*n^5 + (160/3)*n^4 + 56*n^3 + (92/3)*n^2 + (26/3)*n + 1.

Conjectures from Colin Barker, Mar 01 2018: (Start)

G.f.: x*(171 + 1099*x + 1134*x^2 + 150*x^3 + 7*x^4 - x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)