A184574 T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order

14178, 102445, 102445, 545662, 993538, 545662, 2430950, 6803631, 6803631, 2430950, 9496395, 37767705, 57374460, 37767705, 9496395, 33351260, 179122657, 380532059, 380532059, 179122657, 33351260, 107058241, 748499580, 2113138210

Offset

1,1

Comments

Table starts

......14178......102445........545662........2430950.........9496395

.....102445......993538.......6803631.......37767705.......179122657

.....545662.....6803631......57374460......380532059......2113138210

....2430950....37767705.....380532059.....2943827443.....18803004899

....9496395...179122657....2113138210....18803004899....136680720320

...33351260...748499580...10202200416...103444456133....848542379467

..107058241..2816118529...43935544294...503785839330...4626643143791

..318063303..9696377100..171891306894..2213469458762..22587829272879

..883398416.30941723282..619309263773..8896632071640.100176548344077

.2312834051.92420016377.2076328840978.33064363109286.408222405584237

Links

R. H. Hardin, Table of n, a(n) for n = 1..480

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

Formula

Empirical: T(n,k) is a polynomial of degree 3k+16 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..1..1....0..0..0..1....0..0..1..1....0..0..0..0....0..0..0..0
..0..0..1..2....0..0..1..1....0..0..1..1....0..0..0..2....0..0..1..2
..2..3..0..0....0..0..3..3....0..3..1..3....1..2..2..2....0..2..3..2
..2..3..0..1....0..1..2..2....1..3..3..3....3..2..3..0....0..3..3..1

Crossrefs

Sequence in context: A204282 A134610 A104825 * A184566 A184565 A251068

Adjacent sequences: A184571 A184572 A184573 * A184575 A184576 A184577

Keyword

nonn,tabl

Author

R. H. Hardin, general degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Jan 17 2011

Status

approved