A188501 Number of n X 2 binary arrays without the pattern 0 1 0 diagonally, vertically or horizontally.
4, 16, 49, 144, 441, 1369, 4225, 12996, 40000, 123201, 379456, 1168561, 3598609, 11082241, 34128964, 105103504, 323676081, 996791184, 3069714025, 9453478441, 29112890625, 89655929476, 276104007936, 850288696321, 2618545348864
Offset: 1
Keywords
Examples
Some solutions for 3 X 2: ..1..1....0..1....1..1....1..1....0..1....1..0....0..1....1..1....1..1....0..1 ..1..0....1..0....1..1....0..0....0..1....1..0....0..0....0..1....0..1....0..0 ..1..0....1..0....1..0....1..0....1..1....0..1....1..1....1..1....1..0....1..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..200
Formula
Empirical: a(n)=3*a(n-1)-a(n-2)+3*a(n-3)+3*a(n-4)-a(n-5)-a(n-6).
Empirical g.f.: x*(4 + 4*x + 5*x^2 + x^3 - 2*x^4 - x^5) / ((1 - x + 2*x^2 - x^3)*(1 - 2*x - 3*x^2 - x^3)). - Colin Barker, Feb 18 2018
Comments