A221694 Number of 2 X n arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

1, 21, 152, 1336, 11036, 92660, 774380, 6479664, 54200980, 453418640, 3792991120, 31729761276, 265430689860, 2220422566716, 18574626389432, 155383375746468, 1299837358873328, 10873603138412824, 90961568659281764, 760925966163564220

Offset

1,2

Comments

Row 2 of A221693.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 5*a(n-1) + 28*a(n-2) + 9*a(n-3) - 62*a(n-4) - 30*a(n-5) + 64*a(n-6) + 32*a(n-7) - 32*a(n-8) + 32*a(n-9).

Empirical g.f.: x*(1 + 16*x + 19*x^2 - 21*x^3 - 27*x^4 + 36*x^5 + 38*x^6 - 24*x^7 + 24*x^8) / ((1 + 2*x)^2*(1 - 9*x + 4*x^2 + 11*x^3 + 2*x^4 - 22*x^5 + 16*x^6 - 8*x^7)). - Colin Barker, Aug 10 2018

Example

Some solutions for n=3:
..2..1..1....0..2..1....1..1..0....1..2..0....2..1..0....1..0..0....0..2..1
..0..0..2....1..0..2....3..0..1....0..3..0....0..3..0....1..3..1....2..1..0

Crossrefs

Cf. A221693.

Sequence in context: A358994 A239569 A219599 * A229262 A184376 A184368

Adjacent sequences: A221691 A221692 A221693 * A221695 A221696 A221697

Keyword

nonn

Author

R. H. Hardin, Jan 22 2013

Status

approved