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

1,1

Comments

Row 3 of A195278.

Links

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

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)

Example

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

Crossrefs

Cf. A195278.

Sequence in context: A251223 A186868 A185611 * A370299 A016058 A332418

Adjacent sequences: A195276 A195277 A195278 * A195280 A195281 A195282

Keyword

nonn

Author

R. H. Hardin, Sep 14 2011

Status

approved