A250942 T(n,k)=Number of (n+1)X(k+1) 0..2 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

37, 155, 125, 599, 699, 413, 2247, 3355, 2812, 1333, 8189, 15431, 16208, 10528, 4213, 29281, 67595, 87529, 71014, 37477, 13111, 103093, 287045, 442409, 444421, 289407, 128507, 40357, 358683, 1188599, 2130148, 2572787, 2067987, 1115035, 428095

Offset

1,1

Comments

Table starts

......37......155.......599.......2247........8189........29281........103093

.....125......699......3355......15431.......67595.......287045.......1188599

.....413.....2812.....16208......87529......442409......2130148.......9865706

....1333....10528.....71014.....444421.....2572787.....14019652......72722706

....4213....37477....289407....2067987....13550488.....82716842.....475951361

...13111...128507...1115035....8976385....65910564....447407616....2839711239

...40357...428095...4106983...36809498...300230097...2251710502...15686582837

..123271..1394237..14585505..144007880..1294549437..10665462156...81197881457

..374509..4460779..50276307..541598982..5327479262..47958734697..397409857238

.1133503.14073313.169096201.1969991292.21062394646.206139574253.1852256126330

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

Empirical for column k:

k=1: a(n) = 8*a(n-1) -23*a(n-2) +28*a(n-3) -12*a(n-4) for n>6

k=2: [order 7] for n>11

k=3: [order 15] for n>21

k=4: [order 21] for n>29

k=5: [order 27] for n>37

k=6: [order 33] for n>45

k=7: [order 39] for n>53

Empirical for row n:

n=1: a(n) = 6*a(n-1) -6*a(n-2) -15*a(n-3) +14*a(n-4) +12*a(n-5)

n=2: [order 11]

n=3: [order 21]

n=4: [order 38]

n=5: [order 60]

n=6: [order 88]

Example

Some solutions for n=3 k=4
..2..1..0..0..2....0..0..1..1..1....1..2..0..0..2....2..0..0..1..0
..2..1..0..0..2....0..0..1..2..0....2..1..1..1..1....2..0..0..1..0
..2..1..0..1..1....0..0..1..2..0....2..1..2..2..0....2..0..0..2..2
..2..1..0..1..2....1..1..2..1..1....2..1..2..2..0....2..0..0..2..2

Crossrefs

Column 1 is A250891

Sequence in context: A158596 A142688 A178835 * A250943 A142197 A140011

Adjacent sequences: A250939 A250940 A250941 * A250943 A250944 A250945

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 28 2014

Status

approved