A221514 Number of 0..7 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0.
0, 6, 31, 252, 1765, 12872, 92934, 672526, 4864004, 35184566, 254499831, 1840896185, 13315870072, 96318591951, 696707724524, 5039542943168, 36452864937683, 263676961336509, 1907272308179486, 13796001136950442
Offset: 1
Keywords
Examples
Some solutions for n=6 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0 ..3....6....5....3....3....6....7....3....2....2....2....7....7....2....2....4 ..2....5....3....2....2....0....7....2....3....1....3....7....5....3....6....7 ..4....7....0....4....0....6....0....6....5....4....7....1....3....5....1....4 ..5....2....0....5....0....5....4....5....4....7....4....7....6....3....7....4 ..3....5....7....1....4....7....1....0....2....0....2....4....0....0....3....1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = 3*a(n-1) +21*a(n-2) +58*a(n-3) +79*a(n-4) +32*a(n-5) +23*a(n-6) +4*a(n-7) +8*a(n-8).
Empirical g.f.: x^2*(6 + 13*x + 33*x^2 + 10*x^3 + 13*x^4 - 4*x^5 + 4*x^6) / (1 - 3*x - 21*x^2 - 58*x^3 - 79*x^4 - 32*x^5 - 23*x^6 - 4*x^7 - 8*x^8). - Colin Barker, Oct 18 2017
Comments