A184073 Number of (n+1) X 2 0..2 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.

29, 58, 150, 335, 728, 1499, 2968, 5645, 10331, 18242, 31173, 51709, 83492, 131554, 202727, 306142, 453830, 661439, 949082, 1342332, 1873381, 2582381, 3518986, 4744115, 6331957, 8372240, 10972787, 14262383, 18393978, 23548252, 29937569

Offset

1,1

Comments

Column 1 of A184081.

Links

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

Formula

Conjectures from Colin Barker, Apr 12 2018: (Start)

G.f.: x*(29 - 203*x + 672*x^2 - 1363*x^3 + 1895*x^4 - 1939*x^5 + 1573*x^6 - 1117*x^7 + 749*x^8 - 450*x^9 + 209*x^10 - 65*x^11 + 12*x^12 - x^13) / (1 - x)^9.

a(n) = (1290240 - 1768560*n + 1559788*n^2 - 343756*n^3 + 72569*n^4 - 4480*n^5 + 602*n^6 - 4*n^7 + n^8) / 40320 for n>5.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>14.

(End)

Example

Some solutions for 3 X 2:
..0..0....0..1....0..2....0..2....0..0....0..2....0..2....0..1....0..1....0..1
..0..1....0..2....1..0....1..1....0..2....2..0....2..0....0..1....1..1....0..1
..0..1....1..0....2..0....2..0....1..0....2..1....2..0....0..2....1..1....1..1
...
...1.......3.......3.......4.......2.......4.......4.......2.......3.......2...
...2.......3.......3.......4.......3.......5.......4.......3.......4.......3...

Crossrefs

Cf. A184081.

Sequence in context: A249079 A004942 A033904 * A080170 A078848 A055784

Adjacent sequences: A184070 A184071 A184072 * A184074 A184075 A184076

Keyword

nonn

Author

R. H. Hardin, Jan 09 2011

Status

approved