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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A052548(n+1)

Column 2 is A153972(n+1)

Diagonal is A000918(n+2)

Sequence in context: A024746 A111093 A144394 * A315122 A087873 A284238

Adjacent sequences: A250739 A250740 A250741 * A250743 A250744 A250745

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 27 2014

Status

approved