login
A186454
Number of (n+1) X 2 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.
2
16, 21, 42, 61, 106, 151, 245, 359, 567, 840, 1301, 1941, 2977, 4465, 6810, 10247, 15577, 23487, 35635, 53800, 81533, 123193, 186569, 282037, 426954, 645623, 977117, 1477831, 2236287, 3382632, 5118213, 7742397, 11714273, 17721097, 26811194
OFFSET
1,1
COMMENTS
Column 1 of A186462.
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) for n>8.
Empirical g.f.: x*(16 - 11*x + 9*x^3 - 6*x^4 - 3*x^5 + 2*x^6 + x^7) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Feb 28 2018
EXAMPLE
Some solutions for 3 X 2:
..1..0....1..0....1..0....0..1....0..0....1..0....1..0....0..0....0..0....1..0
..1..0....0..0....0..1....0..1....1..0....0..0....0..1....0..0....1..0....1..0
..0..1....0..1....1..0....0..1....0..1....0..0....0..0....0..0....1..1....1..0
CROSSREFS
Cf. A186462.
Sequence in context: A330591 A302167 A376209 * A302638 A302430 A138173
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 22 2011
STATUS
approved