A250742 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nonincreasing x(i,j)-x(i-1,j) in the j direction.

6, 10, 10, 18, 14, 18, 34, 22, 22, 34, 66, 38, 30, 38, 66, 130, 70, 46, 46, 70, 130, 258, 134, 78, 62, 78, 134, 258, 514, 262, 142, 94, 94, 142, 262, 514, 1026, 518, 270, 158, 126, 158, 270, 518, 1026, 2050, 1030, 526, 286, 190, 190, 286, 526, 1030, 2050, 4098, 2054, 1038

Offset: 1

Author

R. H. Hardin, Nov 27 2014

Keywords

• nonn
• tabl

Comments

Table starts

....6...10...18...34...66..130..258..514.1026.2050.4098..8194.16386.32770.65538

...10...14...22...38...70..134..262..518.1030.2054.4102..8198.16390.32774.65542

...18...22...30...46...78..142..270..526.1038.2062.4110..8206.16398.32782.65550

...34...38...46...62...94..158..286..542.1054.2078.4126..8222.16414.32798.65566

...66...70...78...94..126..190..318..574.1086.2110.4158..8254.16446.32830.65598

..130..134..142..158..190..254..382..638.1150.2174.4222..8318.16510.32894.65662

..258..262..270..286..318..382..510..766.1278.2302.4350..8446.16638.33022.65790

..514..518..526..542..574..638..766.1022.1534.2558.4606..8702.16894.33278.66046

.1026.1030.1038.1054.1086.1150.1278.1534.2046.3070.5118..9214.17406.33790.66558

.2050.2054.2062.2078.2110.2174.2302.2558.3070.4094.6142.10238.18430.34814.67582

Examples

			Some solutions for n=4 k=4
..0..0..0..0..0....1..0..1..0..1....0..1..0..0..1....1..1..1..1..1
..0..0..0..0..0....1..0..1..0..1....0..1..0..0..1....1..1..1..1..1
..0..0..0..0..0....1..0..1..0..1....0..1..0..0..1....0..0..0..0..0
..1..1..1..1..1....1..0..1..0..1....0..1..0..0..1....0..0..0..0..0
..1..1..1..1..1....1..0..1..0..1....0..1..0..0..1....1..1..1..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1450

Crossrefs

Column 1 is A052548(n+1)

Column 2 is A153972(n+1)

Diagonal is A000918(n+2)

Formula

The constraints apparently result in horizontally or vertically banded arrays, hence:

Empirical: T(n,k) = 2^(k+1)+2^(n+1)-2

Empirical for column k:

k=1: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 2^(n+1) +2

k=2: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 2^(n+1) +6

k=3: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 2^(n+1) +14

k=4: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 2^(n+1) +30

k=5: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 2^(n+1) +62

k=6: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 2^(n+1) +126

k=7: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 2^(n+1) +254