A250898 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, 127, 125, 403, 431, 413, 1229, 1325, 1450, 1333, 3673, 3867, 4388, 4750, 4213, 10875, 11029, 12387, 14196, 15111, 13111, 32095, 31215, 33821, 39003, 44525, 47061, 40357, 94729, 88421, 91030, 102789, 119359, 136509, 144442, 123271, 280069

Offset

1,1

Comments

Table starts

......37.....127......403.....1229.....3673.....10875.....32095.....94729

.....125.....431.....1325.....3867....11029.....31215.....88421....251819

.....413....1450.....4388....12387....33821.....91030....244200....657443

....1333....4750....14196....39003...102789....265546....680504...1742387

....4213...15111....44525...119359...305429....764315...1893433...4673299

...13111...47061...136509...357335...890199...2168405...5232461..12579759

...40357..144442...412006..1052787..2553537...6060594..14283986..33622407

..123271..439056..1231112..3069907..7243359..16732140..38498188..88810083

..374509.1326285..3657629..8903447.20421217..45832201.102731213.231909787

.1133503.3990883.10837431.25780959.57483879.125162059.272597111.600517559

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k (k=2 recurrence works also for k=1):

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

k=2-7: a(n) = 12*a(n-1) -60*a(n-2) +162*a(n-3) -255*a(n-4) +234*a(n-5) -116*a(n-6) +24*a(n-7) for n>9

Empirical for row n (n=3 recurrence works also for n=1,2):

n=1: a(n) = 9*a(n-1) -31*a(n-2) +51*a(n-3) -40*a(n-4) +12*a(n-5)

n=2: a(n) = 10*a(n-1) -40*a(n-2) +82*a(n-3) -91*a(n-4) +52*a(n-5) -12*a(n-6)

n=3-7: a(n) = 14*a(n-1) -85*a(n-2) +294*a(n-3) -639*a(n-4) +906*a(n-5) -839*a(n-6) +490*a(n-7) -164*a(n-8) +24*a(n-9)

Example

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

Crossrefs

Sequence in context: A044669 A048510 A250891 * A165811 A142331 A250899

Adjacent sequences: A250895 A250896 A250897 * A250899 A250900 A250901

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 28 2014

Status

approved