A224391 T(n,k)=Number of nXk 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing

4, 10, 16, 20, 100, 64, 35, 400, 1000, 256, 56, 1225, 6094, 10000, 1024, 84, 3136, 27790, 86701, 100000, 4096, 120, 7056, 102232, 497958, 1268572, 1000000, 16384, 165, 14400, 319769, 2332222, 8573507, 18794636, 10000000, 65536, 220, 27225, 881519

Offset

1,1

Comments

Table starts

.......4..........10...........20.............35..............56

......16.........100..........400...........1225............3136

......64........1000.........6094..........27790..........102232

.....256.......10000........86701.........497958.........2332222

....1024......100000......1268572........8573507........45648753

....4096.....1000000.....18794636......152271025.......879830242

...16384....10000000....279128617.....2780848289.....17642791909

...65536...100000000...4142692993....51325449985....365858453951

..262144..1000000000..61481903024...949582166068...7713944320142

.1048576.10000000000.912523782542.17572045403455.163629606236587

Links

R. H. Hardin, Table of n, a(n) for n = 1..198

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1)

k=2: a(n) = 10*a(n-1)

k=3: [order 15]

k=4: [order 47]

Empirical: rows n=1..6 are polynomials of degree 3*n for k>0,0,1,4,7,10

Example

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

Crossrefs

Column 1 is A000302

Column 2 is A011557

Row 1 is A000292(n+1)

Row 2 is A001249

Sequence in context: A334115 A265010 A223961 * A224024 A117111 A310508

Adjacent sequences: A224388 A224389 A224390 * A224392 A224393 A224394

Keyword

nonn,tabl

Author

R. H. Hardin Apr 05 2013

Status

approved