A198908 Number of n X 2 0..7 arrays with values 0..7 introduced in row major order and no element equal to any horizontal or vertical neighbor.

1, 4, 34, 500, 10867, 313132, 10856948, 418689772, 17067989413, 715189507700, 30371156968582, 1298083132473604, 55654030558406039, 2389712969490386908, 102686352402421016536, 4414019789796312628796, 189771542890022982723145

Offset: 1

Author

R. H. Hardin, Oct 31 2011

Keywords

• nonn

Comments

Column 2 of A198914.

Examples

			Some solutions with values 0 to 7 for n=5:
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..2..3....2..3....1..2....2..3....2..3....2..3....2..3....2..3....2..3....2..3
..4..5....4..2....3..4....4..5....4..5....4..5....4..5....4..5....4..5....4..5
..0..3....1..5....5..6....2..3....6..7....3..6....6..2....6..1....0..6....6..7
..6..7....6..7....2..7....6..7....7..1....7..3....2..7....5..7....7..1....2..4
		

Links

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

Crossrefs

Cf. A198914.

Formula

Empirical: a(n) = 88*a(n-1) - 2613*a(n-2) + 33232*a(n-3) - 184531*a(n-4) + 400344*a(n-5) - 246519*a(n-6).

Conjectures from Colin Barker, Feb 22 2018: (Start)

G.f.: x*(1 - 84*x + 2295*x^2 - 25272*x^3 + 107312*x^4 - 128772*x^5) / ((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 13*x)*(1 - 21*x)*(1 - 43*x)).

a(n) = (1036945 + 344344*3^n + 75465*7^n + 12040*13^n + 2795*21^n + 91*43^n) / 2817360.

(End)