A221853 Number of 2 X n arrays of occupancy after each element stays put or moves to some horizontal, diagonal or antidiagonal neighbor, without consecutive moves in the same direction.
1, 31, 302, 3437, 37155, 406612, 4434129, 48397883, 528123314, 5763315281, 62892896491, 686329748776, 7489683895265, 81732408497079, 891918279715066, 9733204380907645, 106215187016111667, 1159090627331995148
Offset: 1
Keywords
Examples
Some solutions for n=3: ..3..2..1....2..0..2....0..2..1....0..0..1....2..0..0....2..1..1....0..2..0 ..0..0..0....1..0..1....0..3..0....1..2..2....1..3..0....0..0..2....3..0..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..37
Crossrefs
Cf. A221852.
Formula
Empirical: a(n) = 13*a(n-1) - 14*a(n-2) - 113*a(n-3) + 189*a(n-4) - 10*a(n-5) - 42*a(n-6) + 18*a(n-7) - 2*a(n-8).
Empirical g.f.: x*(1 + 18*x - 87*x^2 + 58*x^3 + 16*x^4 - 8*x^5 - 2*x^6) / (1 - 13*x + 14*x^2 + 113*x^3 - 189*x^4 + 10*x^5 + 42*x^6 - 18*x^7 + 2*x^8). - Colin Barker, Aug 11 2018
Comments