A206687 Number of n X 2 0..3 arrays with no element equal to another within two positions in the same row or column, and new values 0..3 introduced in row major order.
1, 4, 11, 36, 116, 376, 1216, 3936, 12736, 41216, 133376, 431616, 1396736, 4519936, 14626816, 47333376, 153174016, 495681536, 1604059136, 5190844416, 16797925376, 54359228416, 175910158336, 569257230336, 1842155094016, 5961339109376
Offset: 1
Keywords
Examples
All solutions for n=4: ..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1 ..2..3....1..0....2..3....1..0....2..3....1..2....1..2....1..2....1..0 ..1..2....2..3....1..0....2..3....3..2....2..0....3..0....2..3....2..3 ..0..1....3..2....3..1....3..1....1..0....3..1....0..1....0..1....0..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A206692.
Formula
Empirical: a(n) = 2*a(n-1) + 4*a(n-2) for n>4.
Conjectures from Colin Barker, Feb 23 2018: (Start)
G.f.: x*(1 - x)*(1 + x)*(1 + 2*x) / (1 - 2*x - 4*x^2).
a(n) = ((1-sqrt(5))^n*(-5+3*sqrt(5)) + (1+sqrt(5))^n*(5+3*sqrt(5))) / (16*sqrt(5)) for n>2.
(End)
Comments