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

1,1

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

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.

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..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

Crossrefs

Sequence in context: A251834 A157803 A236095 * A186172 A186171 A251043

Adjacent sequences: A186177 A186178 A186179 * A186181 A186182 A186183

Keyword

nonn,tabl

Author

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

Status

approved