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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A221693.
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
Comments