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A186096
T(n,k)=Number of (n+2)X(k+2) 0..4 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order
10
102251, 1252889, 1252889, 11258613, 22559052, 11258613, 83378583, 280102672, 280102672, 83378583, 531218757, 2743553694, 4527262140, 2743553694, 531218757, 2985984444, 22408644868, 55707179395, 55707179395, 22408644868, 2985984444
OFFSET
1,1
COMMENTS
Table starts
........102251.........1252889.........11258613...........83378583
.......1252889........22559052........280102672.........2743553694
......11258613.......280102672.......4527262140........55707179395
......83378583......2743553694......55707179395.......837192826927
.....531218757.....22408644868.....558643720724.....10064164793382
....2985984444....157927508610....4754203179765....101247852066065
...15084070635....983600385660...35285910378578....878623899164100
...69482992431...5510351270895..232998389350277...6723402580436327
..295278398390..28148281162513.1389861134920751..46135247077059665
.1168636004931.132536596243411.7581135805604097.287649593317228144
FORMULA
Empirical: T(n,k) is a polynomial of degree 4k+30 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..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..2....0..0..0..2....0..0..0..2....0..0..1..2....0..0..1..2
..0..1..2..1....1..1..2..2....1..1..2..0....1..2..4..4....0..2..1..2
..2..3..3..4....1..2..0..0....3..4..0..1....1..4..1..3....2..4..3..2
CROSSREFS
Sequence in context: A153050 A203592 A106813 * A186088 A186087 A106814
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, General degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Feb 12 2011
STATUS
approved