A195249 Number of lower triangles of a 3 X 3 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by two or less.

64, 729, 1682, 2729, 3776, 4823, 5870, 6917, 7964, 9011, 10058, 11105, 12152, 13199, 14246, 15293, 16340, 17387, 18434, 19481, 20528, 21575, 22622, 23669, 24716, 25763, 26810, 27857, 28904, 29951, 30998, 32045, 33092, 34139, 35186, 36233, 37280, 38327

Offset: 1

Author

R. H. Hardin, Sep 13 2011

Keywords

• nonn

Comments

Row 3 of A195248.

Examples

			Some solutions for n=5:
..2......1......0......0......4......5......1......1......5......3
..3.4....2.3....2.0....0.2....5.4....3.5....1.3....2.3....3.3....2.2
..4.4.4..2.1.2..1.1.1..1.1.3..4.4.5..5.5.3..2.1.3..4.3.4..2.3.3..0.0.2
		

Links

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

Crossrefs

Cf. A195248.

Formula

Empirical: a(n) = 1047*n - 1459 for n>2.

Conjectures from Colin Barker, May 06 2018: (Start)

G.f.: x*(64 + 601*x + 288*x^2 + 94*x^3) / (1 - x)^2.

a(n) = 2*a(n-1) - a(n-2) for n>4.

(End)