A186180 T(n,k)=Number of (n+2)X(k+2) 0..5 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

520017, 10084236, 10084236, 143369699, 311128593, 143369699, 1662436696, 6520730198, 6520730198, 1662436696, 16382439469, 105970767207, 188034884094, 105970767207, 16382439469, 140871930232, 1414199542732, 4041778238254

Offset: 1

Author

R. H. Hardin, General degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Feb 13 2011

Keywords

• nonn
• tabl

Comments

Table starts

..........520017..........10084236............143369699............1662436696

........10084236.........311128593...........6520730198..........105970767207

.......143369699........6520730198.........188034884094.........4041778238254

......1662436696......105970767207........4041778238254.......111203560772547

.....16382439469.....1414199542732.......69471558136868......2391923493659465

....140871930232....16059530994398......995828085723859.....42174821764604242

...1078197169699...159099595031390....12251749347425002....629512200937395977

...7459396065112..1400823449171621...132151619698400257...8143852416376007571

..47221234070168.11121210203531892..1270399513311212137..92981285763140685886

.276218909139304.80539662788823416.11027904404610778911.950506396177707075676

Examples

			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..3....0..0..0..0....0..0..0..0....0..0..0..3....0..0..0..0
..0..0..0..5....0..0..1..2....0..1..1..4....0..1..5..1....0..0..2..3
..0..1..1..0....1..2..0..2....3..1..4..1....5..4..4..5....0..2..5..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..178
• R. H. Hardin, Polynomials for columns 1-5

Formula

Empirical: T(n,k) is a polynomial of degree 5k+50 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.