A183364 Number of n X 2 binary arrays with no element equal to the sum mod 3 of its horizontal and vertical neighbors.

2, 3, 5, 12, 21, 41, 84, 171, 355, 732, 1517, 3165, 6608, 13809, 28871, 60398, 126425, 264681, 554188, 1160473, 2430233, 5089614, 10659415, 22324873, 46757436, 97930229, 205109405, 429591772, 899761459, 1884515059, 3947047760, 8266953369

Offset

1,1

Comments

Column 2 of A183368.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 2*a(n-1) + a(n-3) - 4*a(n-6) - 3*a(n-7) + a(n-10).

Empirical g.f.: x*(1 + x)*(2 - 3*x + 2*x^2 - 2*x^3 - 4*x^4 - 2*x^5 + x^8) / (1 - 2*x - x^3 + 4*x^6 + 3*x^7 - x^10). - Colin Barker, Mar 28 2018

Example

Some solutions for 5 X 2:
..0..0....1..0....0..1....0..1....0..0....1..1....1..1....0..1....1..0....1..1
..1..1....0..0....0..0....1..0....1..1....1..1....1..1....1..0....0..0....1..1
..1..1....1..1....1..1....0..0....1..1....1..1....0..0....0..0....0..1....1..1
..0..0....1..1....1..1....0..1....1..1....1..1....1..0....1..1....0..0....0..0
..1..0....1..1....1..1....1..0....1..1....0..0....0..1....1..1....1..0....1..0

Crossrefs

Cf. A183368.

Sequence in context: A089891 A282237 A004689 * A124370 A003428 A191626

Adjacent sequences: A183361 A183362 A183363 * A183365 A183366 A183367

Keyword

nonn

Author

R. H. Hardin, Jan 04 2011

Status

approved