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A186915 T(n,k)=Number of (n+2)X(k+2) 0..6 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order 10
2066505, 59969593, 59969593, 1276581035, 2974946682, 1276581035, 22000126445, 99241308567, 99241308567, 22000126445, 319741716426, 2536761070723, 4813465754996, 2536761070723, 319741716426, 4028133387613, 52666517720011 (list; table; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A206667 A251512 A113568 * A186907 A186906 A335398
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

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Last modified March 1 22:23 EST 2024. Contains 370443 sequences. (Running on oeis4.)