A223355 Rolling cube footprints: number of n X 6 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or antidiagonal neighbor moves across a corresponding cube edge.
1024, 1327104, 1764753408, 2356125106176, 3147420753985536, 4204783428144463872, 5617417467128419713024, 7504647859211051911348224, 10025914758161450104466178048, 13394228581283493899583803621376
Offset: 1
Keywords
Examples
Some solutions for n=3: 0 3 0 3 4 2 0 3 0 2 0 3 0 3 0 2 5 1 0 3 0 1 0 1 0 3 0 3 0 4 0 3 0 3 0 3 0 3 0 4 2 1 0 3 0 2 5 4 0 3 0 1 2 4 0 3 0 3 5 3 0 3 0 1 3 4 0 3 0 4 5 3
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A223357.
Formula
Empirical: a(n) = 1600*a(n-1) - 368640*a(n-2) + 21233664*a(n-3).
Empirical g.f.: 1024*x*(1 - 304*x + 18432*x^2) / (1 - 1600*x + 368640*x^2 - 21233664*x^3). - Colin Barker, Aug 19 2018
Comments