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

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

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

R. H. Hardin, Polynomials for columns 1-8

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

Adjacent sequences: A186093 A186094 A186095 * A186097 A186098 A186099

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