A250783 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 nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

9, 21, 18, 46, 46, 36, 99, 106, 96, 72, 209, 238, 230, 196, 144, 436, 518, 534, 482, 396, 288, 901, 1106, 1194, 1152, 990, 796, 576, 1849, 2326, 2604, 2640, 2426, 2010, 1596, 1152, 3774, 4838, 5568, 5882, 5688, 5028, 4054, 3196, 2304, 7671, 9978, 11732, 12796

Offset: 1

Author

R. H. Hardin, Nov 27 2014

Keywords

• nonn
• tabl

Comments

Table starts

....9....21....46....99....209....436.....901....1849....3774.....7671....15541

...18....46...106...238....518...1106....2326....4838....9978....20446....41686

...36....96...230...534...1194...2604....5568...11732...24442....50482...103566

...72...196...482..1152...2640...5882...12796...27344...57610...120060...248072

..144...396...990..2426...5688..12950...28692...62274..132890...279864...583196

..288...796..2010..5028..12036..27986...63184..139436..301786...643164..1353544

..576..1596..4054.10306..25126..59590..137082..307762..676266..1460260..3107536

.1152..3196..8146.20960..51904.125334..293588..670608.1496970..3278004..7061504

.2304..6396.16334.42394.106344.260916..621664.1444162.3275574..7278104.15884220

.4608.12796.32714.85420.216500.538538.1303276.3076788.7089558.15987988.35370676

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..544

Crossrefs

Column 1 is A005010(n-1)

Row 1 is A027973(n+1)

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1); a(n) = 9*2^(n-1)

k=2: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 25*2^(n-1) -4

k=3: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3)

k=4: a(n) = 6*a(n-1) -14*a(n-2) +16*a(n-3) -9*a(n-4) +2*a(n-5)

k=5: a(n) = 8*a(n-1) -27*a(n-2) +50*a(n-3) -55*a(n-4) +36*a(n-5) -13*a(n-6) +2*a(n-7)

k=6: [order 9]

k=7: [order 11]

Empirical for row n:

n=1: a(n) = 3*a(n-1) -a(n-2) -2*a(n-3)

n=2: a(n) = 4*a(n-1) -4*a(n-2) -a(n-3) +2*a(n-4)

n=3: a(n) = 5*a(n-1) -8*a(n-2) +3*a(n-3) +3*a(n-4) -2*a(n-5)

n=4: a(n) = 5*a(n-1) -7*a(n-2) -2*a(n-3) +11*a(n-4) -5*a(n-5) -3*a(n-6) +2*a(n-7)

n=5: [order 8]

n=6: [order 9]

n=7: [order 10]