A204678 Number of n X 1 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.
1, 2, 4, 12, 40, 143, 528, 1979, 7466, 28246, 106992, 405481, 1537042, 5826959, 22091016, 83752328, 317527448, 1203835147, 4564081020, 17303737555, 65603438014, 248721498050, 942974761824, 3575088704597, 13554190277870
Offset: 1
Keywords
Examples
Some solutions for n=5: ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0 ..1....1....1....0....1....0....0....1....0....1....0....0....0....1....1....0 ..1....2....0....1....0....1....1....0....1....1....1....1....1....0....0....1 ..0....1....2....0....0....0....0....1....0....0....0....1....0....0....0....0 ..0....0....0....0....1....2....0....0....0....0....0....0....1....1....1....0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = 4*a(n-1) + a(n-2) - 6*a(n-3) - 3*a(n-4) for n>6.
Empirical g.f.: x*(1 + x)*(1 - 3*x - 2*x^2 + 2*x^3 + x^4) / ((1 - x - x^2)*(1 - 3*x - 3*x^2)). - Colin Barker, Feb 19 2018
Comments