A184063 Number of (n+1) X 2 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.

7, 11, 20, 34, 54, 81, 116, 160, 214, 279, 356, 446, 550, 669, 804, 956, 1126, 1315, 1524, 1754, 2006, 2281, 2580, 2904, 3254, 3631, 4036, 4470, 4934, 5429, 5956, 6516, 7110, 7739, 8404, 9106, 9846, 10625, 11444, 12304, 13206, 14151, 15140, 16174, 17254

Offset

1,1

Comments

Column 1 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*(7 - 17*x + 18*x^2 - 8*x^3 + x^4) / (1 - x)^4.

a(n) = (n^3 + 6*n^2 + 5*n + 24) / 6 for n>1.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.

(End)

Example

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

Crossrefs

Cf. A184071.

Sequence in context: A321806 A057190 A106674 * A076854 A356710 A194828

Adjacent sequences: A184060 A184061 A184062 * A184064 A184065 A184066

Keyword

nonn

Author

R. H. Hardin, Jan 09 2011

Status

approved