A231264 Number of (2+1) X (n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.
6, 15, 32, 83, 211, 557, 1471, 3909, 10387, 27617, 73419, 195197, 518979, 1379897, 3669051, 9755861, 25940515, 68974961, 183402043, 487659661, 1296670403, 3447803113, 9167594299, 24376331077, 64815862051, 172343243361, 458255009275
Offset: 1
Keywords
Examples
Some solutions for n=3: ..0..0..0..0....0..0..0..1....0..0..0..0....0..0..0..0....0..0..0..0 ..0..0..1..1....0..0..1..1....1..1..2..2....0..0..0..0....1..1..1..0 ..1..1..1..1....0..1..1..1....1..2..2..2....1..1..1..1....1..1..0..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = 4*a(n-1) -2*a(n-2) -8*a(n-3) +11*a(n-4) -4*a(n-6) -4*a(n-7) -4*a(n-8) +8*a(n-9).
Empirical g.f.: x*(6 - 9*x - 16*x^2 + 33*x^3 - 3*x^4 - 30*x^5 + x^6 - 2*x^7 + 40*x^8) / ((1 - x)*(1 + x)*(1 - 2*x + 2*x^2)*(1 - 2*x^2)*(1 - 2*x - x^2 - 2*x^3)). - Colin Barker, Feb 16 2018
Comments