A239530 Number of (n+1) X (1+1) 0..2 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..2 introduced in row major order.
1, 1, 6, 13, 47, 128, 405, 1181, 3598, 10705, 32259, 96544, 290009, 869417, 2609238, 7826117, 23480935, 70438624, 211322637, 633956965, 1901888606, 5705637161, 17116957851, 51350798528, 154052516977, 462157354513, 1386472381350
Offset: 1
Keywords
Examples
Some solutions for n=5: ..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1 ..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1 ..0..2....2..0....1..0....1..0....1..0....0..2....2..0....2..1....2..1....1..0 ..0..2....2..0....1..0....1..0....1..0....0..2....2..0....2..1....2..0....1..0 ..1..2....1..0....0..1....1..0....2..1....2..0....0..2....0..2....1..0....0..2 ..1..2....1..0....0..1....1..0....2..1....2..0....0..2....0..2....1..0....0..2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Column 1 of A239537.
Formula
Empirical: a(n) = 2*a(n-1) + 4*a(n-2) - 3*a(n-3).
Conjectures from Colin Barker, Oct 26 2018: (Start)
G.f.: x*(1 - x) / ((1 - 3*x)*(1 + x - x^2)).
a(n) = (10*3^n + 2^(-n)*((-1+sqrt(5))^n*(-5+4*sqrt(5)) - (-1-sqrt(5))^n*(5+4*sqrt(5)))) / 55.
(End)