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A185435
T(n,k)=Number of (n+2)X(k+2) 0..7 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order
10
6842284, 284037544, 284037544, 8653394212, 21536560306, 8653394212, 212298419684, 1090205284029, 1090205284029, 212298419684, 4370405405266, 41910604337378, 84722449466168, 41910604337378, 4370405405266
OFFSET
1,1
COMMENTS
Table starts
.............6842284..............284037544................8653394212
...........284037544............21536560306.............1090205284029
..........8653394212..........1090205284029............84722449466168
........212298419684.........41910604337378..........4772160687307074
.......4370405405266.......1297535366114472........209290512833668811
......77657199293322......33575010264022917.......7468756070356586903
....1216284173329482.....745543958045415621.....223694029250999654095
...17062128865116751...14492443009379677098....5755145891541173071730
..217083576402029968..250496452202647761530..129520045203909930078682
.2530473438240068012.3898612401674733619729.2587203198419699686906895
FORMULA
Empirical: T(n,k) is a polynomial of degree 7k+112, for fixed k
Let T(n,k,z) be the number of (n+2)X(k+2) 0..z arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order
Then empirically T(n,k,z) is a polynomial of degree z*k + z*(z+1)*(z+5)/6 in n, for fixed k.
EXAMPLE
Some solutions for 5X4
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..4....0..0..0..0....0..0..0..0....0..0..0..4
..0..1..1..2....0..0..2..3....0..1..4..5....0..0..5..6....0..0..6..7
..0..3..7..3....0..7..0..5....0..2..1..6....2..2..6..4....0..4..3..0
CROSSREFS
Sequence in context: A088238 A079015 A372085 * A185427 A185426 A250457
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, General degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Jan 27 2011
STATUS
approved