login
A183721
1/12 the number of (n+1) X 2 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.
1
0, 1, 12, 87, 537, 3070, 16731, 88331, 455804, 2311983, 11571209, 57295330, 281223411, 1370286715, 6635743136, 31964799247, 153273890393, 732031932806, 3483896304443, 16529018119643, 78202676604548, 369073777749215
OFFSET
1,3
COMMENTS
Column 1 of A183729.
LINKS
FORMULA
Empirical: a(n) = 8*a(n-1) - 11*a(n-2) - 23*a(n-3) + 6*a(n-4) + 7*a(n-5) - 2*a(n-6).
Empirical g.f.: x^2*(1 + 2*x - x^2)^2 / ((1 + x)*(1 - 5*x + 2*x^2)*(1 - 4*x - 2*x^2 + x^3)). - Colin Barker, Apr 04 2018
EXAMPLE
All solutions with the first block increasing clockwise for 3 X 2:
..3..4....1..2....4..5....2..3....5..0....0..1
..2..5....0..3....3..0....1..4....4..1....5..2
..1..0....5..4....2..1....0..5....3..2....4..3
...
...R.......R.......R.......R.......R.......R...
...R.......R.......R.......R.......R.......R...
CROSSREFS
Cf. A183729.
Sequence in context: A243248 A046023 A369421 * A180797 A137207 A206765
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 06 2011
STATUS
approved