A195237 Number of lower triangles of a 7 X 7 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

268435456, 1663418313, 3601738548, 5618308863, 7640055854, 9661943973, 11683832092, 13705720211, 15727608330, 17749496449, 19771384568, 21793272687, 23815160806, 25837048925, 27858937044, 29880825163, 31902713282, 33924601401

Offset: 1

Author

R. H. Hardin, Sep 13 2011

Keywords

• nonn

Comments

Row 7 of A195232.

Examples

			Some solutions for n=6 with 0 and 6:
..6..............0..............0..............0..............6
..5.5............1.1............1.1............1.1............5.5
..4.4.4..........2.2.2..........1.2.2..........2.2.2..........4.4.4
..4.3.3.3........3.3.3.3........1.1.2.3........2.3.3.3........3.3.3.3
..4.3.2.2.2......3.4.3.4.4......0.1.2.3.4......3.2.3.3.4......2.2.2.2.2
..3.3.3.2.2.1....3.4.4.4.5.5....1.1.2.3.4.5....2.3.2.3.4.5....1.2.2.2.1.1
..4.3.3.2.1.1.0..4.4.4.5.4.5.6..2.1.2.3.4.5.6..3.2.2.3.4.5.6..2.2.2.2.2.1.0
		

Links

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

Crossrefs

Cf. A195232.

Formula

Empirical: a(n) = 2021888119*n - 2469384741 for n>4.

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

G.f.: x*(268435456 + 1126547401*x + 543337378*x^2 + 78250080*x^3 + 5176676*x^4 + 141128*x^5) / (1 - x)^2.

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

(End)