login
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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 09 2011
STATUS
approved