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

1,2

Comments

Column 2 of A198914.

Links

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

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)

Example

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

Crossrefs

Cf. A198914.

Sequence in context: A274244 A002105 A198717 * A207864 A222077 A081972

Adjacent sequences: A198905 A198906 A198907 * A198909 A198910 A198911

Keyword

nonn

Author

R. H. Hardin, Oct 31 2011

Status

approved