OFFSET
1,1
COMMENTS
Table starts
...........2066505.............59969593.............1276581035
..........59969593...........2974946682............99241308567
........1276581035..........99241308567..........4813465754996
.......22000126445........2536761070723........171334955820947
......319741716426.......52666517720011.......4805827783188400
.....4028133387613......921058887545363.....110909004238159456
....44902749582723....13921822487031205....2169936652932512523
...449959668016830...185414592506642580...36804096662464163093
..4103914508092780..2208956268019713255..550615265988952206164
.34409633745323847.23828517723857362267.7367827886026471340866
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..126
R. H. Hardin, Polynomials for columns 1-5
FORMULA
Empirical: T(n,k) is a polynomial of degree 6k+77, 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..0....0..0..0..0....0..0..0..0....0..0..0..0
..1..1..3..3....1..1..1..5....0..1..4..6....0..1..5..6....1..2..4..4
..1..4..5..5....5..5..5..6....0..3..2..5....1..5..6..0....5..6..0..1
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, general degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Feb 28 2011
STATUS
approved