A221513 Number of 0..6 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0.
0, 5, 21, 150, 884, 5513, 33860, 208756, 1285694, 7921082, 48795589, 300602292, 1851824780, 11407972817, 70277580919, 432937512858, 2667065000212, 16430167559715, 101216282472118, 623532037268338, 3841202145282104
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 ..4....4....3....5....2....6....2....3....4....2....5....4....4....6....5....5 ..3....0....0....2....4....1....0....6....4....4....4....0....1....2....5....1 ..1....0....4....5....0....4....0....2....0....0....1....3....4....0....2....2 ..2....4....0....1....1....3....5....0....4....4....2....5....0....0....3....5 ..4....1....3....4....3....5....2....5....0....2....6....0....3....6....0....2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = 3*a(n-1) +14*a(n-2) +29*a(n-3) +28*a(n-4) +a(n-5) +27*a(n-6) +8*a(n-7) +2*a(n-8).
Empirical g.f.: x^2*(5 + 6*x + 17*x^2 - 5*x^3 + 12*x^4 + 2*x^5 + 2*x^6) / (1 - 3*x - 14*x^2 - 29*x^3 - 28*x^4 - x^5 - 27*x^6 - 8*x^7 - 2*x^8). - Colin Barker, Oct 18 2017
Comments