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

Author

R. H. Hardin Apr 05 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000302

Column 2 is A011557

Row 1 is A000292(n+1)

Row 2 is A001249

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