A259243 Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0111.
9, 21, 48, 111, 255, 588, 1353, 3117, 7176, 16527, 38055, 87636, 201801, 464709, 1070112, 2464239, 5674575, 13067292, 30091017, 69292893, 159565944, 367444623, 846142455, 1948476324, 4486903689, 10332332661, 23793043728, 54790041711
Offset: 1
Keywords
Examples
Some solutions for n=4: ..1..0....1..1....1..0....0..1....1..0....1..1....1..1....1..0....0..1....0..1 ..1..0....1..0....1..1....1..1....1..1....0..1....0..1....1..1....1..1....1..1 ..1..1....1..0....0..1....0..1....0..0....1..1....0..1....0..1....1..0....0..0 ..0..0....1..1....1..1....1..1....1..1....0..1....1..1....1..1....1..1....1..1 ..1..1....0..1....0..0....0..1....0..0....0..1....0..0....1..0....1..0....0..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Column 1 of A259250.
Formula
Empirical: a(n) = a(n-1) + 3*a(n-2).
Conjectures from Colin Barker, Dec 24 2018: (Start)
G.f.: 3*x*(3 + 4*x) / (1 - x - 3*x^2).
a(n) = (2^(-n)*((1-sqrt(13))^n*(-7+2*sqrt(13)) + (1+sqrt(13))^n*(7+2*sqrt(13)))) / sqrt(13).
(End)