A221541 Number of 0..7 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.
0, 7, 44, 350, 2658, 20386, 156098, 1195561, 9156379, 70126074, 537074685, 4113296146, 31502516844, 241268447450, 1847803587081, 14151780448318, 108384295414048, 830083220654363, 6357361558503534, 48689149448999134
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....7....6....3....0....4....3....2....0....0....0....2....4....2....3....4 ..2....5....3....2....6....1....4....7....3....4....6....6....0....5....2....1 ..4....6....6....4....6....4....1....0....6....4....5....6....2....0....0....7 ..4....2....7....1....7....3....7....2....3....0....5....6....2....6....4....4 ..6....7....5....7....4....6....4....6....0....3....5....1....7....2....0....1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = 7*a(n-1) +4*a(n-2) +5*a(n-3) +20*a(n-4) +20*a(n-5) +23*a(n-6) -6*a(n-7) +3*a(n-8).
Empirical g.f.: x^2*(7 - 5*x + 14*x^2 - 3*x^3 + 20*x^4 - 6*x^5) / (1 - 7*x - 4*x^2 - 5*x^3 - 20*x^4 - 20*x^5 - 23*x^6 + 6*x^7 - 3*x^8). - Colin Barker, Oct 18 2017
Comments