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

1,1

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A005010(n-1)

Row 1 is A027973(n+1)

Sequence in context: A157812 A218164 A161326 * A259250 A251219 A284131

Adjacent sequences: A250780 A250781 A250782 * A250784 A250785 A250786

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 27 2014

Status

approved