OFFSET
1,1
COMMENTS
Table starts
....1169.....4594.....13659......34779......79743......169052.......336690
....4594....21834.....76309.....225672.....594798.....1433903......3212372
...13659....76309....308692....1043186....3097348.....8297059.....20411234
...34779...225672...1043186....3959167...12990375....37961900....100908633
...79743...594798...3097348...12990375...46410729...146203201....416227164
..169052..1433903...8297059...37961900..146203201...493061605...1497314456
..336690..3212372..20411234..100908633..416227164..1497314456...4845252741
..636698..6763143..46732687..247920339.1090826214..4179700035..14425457557
.1151966.13496424.100636591..570069808.2669230399.10893560939..40183952539
.2005704.25706057.205574323.1239033996.6166331968.26828743607.106069534256
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..1404
R. H. Hardin, Polynomials for columns 1-8
FORMULA
Empirical: T(n,k) is a polynomial of degree 2k+7 in n, 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..1..1....0..0..0..1....0..0..0..2....0..0..0..1
..0..0..0..2....1..1..1..2....0..0..0..1....1..1..1..2....0..0..1..2
..0..0..1..2....1..1..1..2....0..0..0..1....1..1..1..2....0..1..2..2
..0..1..1..2....1..1..2..1....1..1..2..1....1..1..1..2....0..2..0..0
..2..1..1..2....1..2..0..2....2..2..1..0....1..1..2..2....0..2..2..2
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, General degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Jan 28 2011
STATUS
approved