A184548 T(n,k)=Number of (n+2)X(k+2) binary arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order

45, 89, 89, 147, 193, 147, 220, 340, 340, 220, 309, 537, 631, 537, 309, 415, 792, 1048, 1048, 792, 415, 539, 1114, 1627, 1837, 1627, 1114, 539, 682, 1513, 2413, 3024, 3024, 2413, 1513, 682, 845, 2000, 3461, 4774, 5313, 4774, 3461, 2000, 845, 1029, 2587, 4837

Offset

1,1

Comments

Table starts

...45...89..147...220...309....415....539....682.....845....1029....1235

...89..193..340...537...792...1114...1513...2000....2587....3287....4114

..147..340..631..1048..1627...2413...3461...4837....6619....8898...11779

..220..537.1048..1837..3024...4774...7307..10909...15944...22867...32238

..309..792.1627..3024..5313...8989..14767..23648...36997...56634...84939

..415.1114.2413..4774..8989..16345..28844..49489...82648..134509..213640

..539.1513.3461..7307.14767..28844..54543..99872..177207..305112..510719

..682.2000.4837.10909.23648..49489..99872.194245..364432..660821.1160932

..845.2587.6619.15944.36997..82648.177207.364432..719905.1369596.2516995

.1029.3287.8898.22867.56634.134509.305112.660821.1369596.2725367.5225554

Links

R. H. Hardin, Table of n, a(n) for n = 1..9378

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

Formula

Empirical: T(n,k) is a polynomial of degree k+2 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..1....0..0..0..1....0..0..0..0....0..0..0..1....0..0..0..0
..0..0..1..1....0..0..0..1....0..0..0..0....0..0..1..1....0..0..0..0
..0..0..1..1....0..0..1..1....0..0..0..0....0..0..1..1....0..0..0..0
..0..1..0..0....0..1..0..1....0..0..0..1....0..1..1..1....0..0..1..1
..1..1..0..0....1..1..0..1....1..1..1..0....0..1..1..1....1..1..0..1

Crossrefs

Sequence in context: A043964 A140380 A183625 * A184540 A115827 A070002

Adjacent sequences: A184545 A184546 A184547 * A184549 A184550 A184551

Keyword

nonn,tabl

Author

R. H. Hardin, general degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Jan 16 2011

Status

approved