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A224391
T(n,k)=Number of nXk 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing
12
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Apr 05 2013
STATUS
approved