A195000 Number of lower triangles of a 4 X 4 0..n array with each element differing from all of its horizontal and vertical neighbors by one.

2, 80, 248, 458, 672, 888, 1104, 1320, 1536, 1752, 1968, 2184, 2400, 2616, 2832, 3048, 3264, 3480, 3696, 3912, 4128, 4344, 4560, 4776, 4992, 5208, 5424, 5640, 5856, 6072, 6288, 6504, 6720, 6936, 7152, 7368, 7584, 7800, 8016, 8232, 8448, 8664, 8880, 9096

Offset: 1

Author

R. H. Hardin, Sep 07 2011

Keywords

• nonn

Comments

Row 4 of A194998.

Examples

			Some solutions for n=4:
..1........4........3........4........2........1........1........0
..2.1......3.2......2.3......3.2......3.4......0.1......2.1......1.2
..1.0.1....2.1.2....3.4.3....2.1.2....2.3.4....1.2.1....3.2.3....2.3.2
..0.1.0.1..1.2.3.4..2.3.2.1..1.0.1.0..3.4.3.2..2.1.2.1..2.3.2.3..3.2.1.0
		

Links

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

Crossrefs

Cf. A194998.

Formula

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

G.f.: 2*x*(1 + 38*x + 45*x^2 + 21*x^3 + 2*x^4 + x^5) / (1 - x)^2.

a(n) = 24*(9*n - 17) for n>4.

a(n) = 2*a(n-1) - a(n-2) for n>6.

(End)