A184065 Number of (n+1) X 4 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.

20, 36, 130, 382, 924, 1884, 3463, 5800, 9065, 13397, 18940, 25837, 34232, 44269, 56092, 69845, 85672, 103717, 124124, 147037, 172600, 200957, 232252, 266629, 304232, 345205, 389692, 437837, 489784, 545677, 605660, 669877, 738472, 811589

Offset

1,1

Comments

Column 3 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*(20 - 44*x + 106*x^2 - 2*x^3 + 52*x^4 - 4*x^5 + 73*x^6 - 62*x^7 + 31*x^8 - 31*x^9 + 5*x^10 - x^11 + x^12) / (1 - x)^4.

a(n) = 757 + 14*n - 115*n^2 + 24*n^3 for n>9.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>13.

(End)

Example

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

Crossrefs

Cf. A184071.

Sequence in context: A174628 A316098 A308664 * A259734 A294736 A217427

Adjacent sequences: A184062 A184063 A184064 * A184066 A184067 A184068

Keyword

nonn

Author

R. H. Hardin, Jan 09 2011

Status

approved