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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
14
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 27 2014
STATUS
approved