A221680 Number of 0..5 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.
0, 2, 5, 32, 133, 636, 2856, 13169, 60120, 275632, 1261451, 5777107, 26449970, 121113272, 554546205, 2539172736, 11626346343, 53234805475, 243751618738, 1116090939600, 5110360772166, 23399338403512, 107140971422686
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 ..0....0....0....0....0....0....1....0....0....0....1....0....1....1....0....0 ..5....1....4....3....3....1....2....4....1....1....2....1....1....1....0....4 ..4....3....4....3....2....2....3....5....1....2....3....1....2....1....0....4 ..5....3....2....0....1....3....2....2....1....0....5....1....3....1....1....3 ..5....3....2....1....1....4....1....2....0....1....4....1....2....1....0....4
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = 4*a(n-1) +3*a(n-2) -6*a(n-3) +19*a(n-4) +5*a(n-5) +a(n-6).
Empirical g.f.: x^2*(2 - 3*x + 6*x^2 + 2*x^3) / (1 - 4*x - 3*x^2 + 6*x^3 - 19*x^4 - 5*x^5 - x^6). - Colin Barker, Oct 19 2017
Comments