A184064 Number of (n+1) X 3 binary arrays with rows and columns in nondecreasing order and with no 2 X 2 subblock sum differing from a horizontal or vertical neighbor subblock sum by more than one.

11, 16, 36, 73, 134, 225, 354, 529, 758, 1049, 1410, 1849, 2374, 2993, 3714, 4545, 5494, 6569, 7778, 9129, 10630, 12289, 14114, 16113, 18294, 20665, 23234, 26009, 28998, 32209, 35650, 39329, 43254, 47433, 51874, 56585, 61574, 66849, 72418, 78289, 84470

Offset

1,1

Comments

Column 2 of A184071.

Links

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

Formula

Conjectures from Colin Barker, Apr 11 2018: (Start)

G.f.: x*(11 - 28*x + 38*x^2 - 19*x^3 + 5*x^4 - x^5 + 2*x^6) / (1 - x)^4.

a(n) = (4*n^3 - 15*n^2 + 74*n - 93) / 3 for n>3.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>7.

(End)

Example

Some solutions for 4 X 3:
..0..0..1....1..1..1....0..0..0....0..0..1....0..0..0....0..1..1....0..1..1
..0..1..0....1..1..1....0..0..1....0..1..0....0..0..0....1..0..1....1..0..1
..1..0..1....1..1..1....0..1..0....0..1..1....0..0..0....1..0..1....1..0..1
..1..1..1....1..1..1....0..1..0....1..1..0....0..0..0....1..1..0....1..1..1
...
...1..2.......4..4.......0..1.......1..2.......0..0.......2..3.......2..3...
...2..2.......4..4.......1..2.......2..3.......0..0.......2..2.......2..2...
...3..3.......4..4.......2..2.......3..3.......0..0.......3..2.......3..3...

Crossrefs

Cf. A184071.

Sequence in context: A327752 A128835 A316171 * A302207 A032311 A032221

Adjacent sequences: A184061 A184062 A184063 * A184065 A184066 A184067

Keyword

nonn

Author

R. H. Hardin, Jan 09 2011

Status

approved