A184044 1/9 the number of (n+1) X 6 0..2 arrays with all 2 X 2 subblocks having the same four values.
81, 87, 97, 117, 153, 225, 361, 633, 1161, 2217, 4297, 8457, 16713, 33225, 66121, 131913, 263241, 525897, 1050697, 2100297, 4198473, 8394825, 16785481, 33566793, 67125321, 134242377, 268468297, 536920137, 1073807433, 2147582025, 4295098441, 8590131273, 17180131401
Offset: 1
Keywords
Examples
Some solutions for 5 X 6: ..2..0..1..0..2..1....2..1..2..0..2..0....0..2..1..0..1..0....1..2..1..0..1..0 ..1..1..2..1..1..0....2..0..2..1..2..1....1..0..0..2..0..2....2..0..2..2..2..2 ..2..0..1..0..2..1....2..1..2..0..2..0....0..2..1..0..1..0....1..2..1..0..1..0 ..1..1..2..1..1..0....2..0..2..1..2..1....1..0..0..2..0..2....2..0..2..2..2..2 ..2..0..1..0..2..1....2..1..2..0..2..0....0..2..1..0..1..0....1..2..1..0..1..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..200
Crossrefs
Column 5 of A184048.
Formula
Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
Conjectures from Colin Barker, Apr 10 2018: (Start)
G.f.: x*(81 - 156*x - 164*x^2 + 312*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
a(n) = 3*2^(n/2) + 2^(n+1) + 73 for n even.
a(n) = 2^(n+1) + 2^((n+3)/2) + 73 for n odd. (End)
Conjectured e.g.f.: 2*cosh(2*x) + 3*cosh(sqrt(2)*x) + 73*sinh(x) + cosh(x)*(73 + 4*sinh(x)) + 2*sqrt(2)*sinh(sqrt(2)*x) - 78. - Stefano Spezia, Aug 01 2025