A185477 T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order

1169, 4594, 4594, 13659, 21834, 13659, 34779, 76309, 76309, 34779, 79743, 225672, 308692, 225672, 79743, 169052, 594798, 1043186, 1043186, 594798, 169052, 336690, 1433903, 3097348, 3959167, 3097348, 1433903, 336690, 636698, 3212372, 8297059

Offset

1,1

Comments

Table starts

....1169.....4594.....13659......34779......79743......169052.......336690

....4594....21834.....76309.....225672.....594798.....1433903......3212372

...13659....76309....308692....1043186....3097348.....8297059.....20411234

...34779...225672...1043186....3959167...12990375....37961900....100908633

...79743...594798...3097348...12990375...46410729...146203201....416227164

..169052..1433903...8297059...37961900..146203201...493061605...1497314456

..336690..3212372..20411234..100908633..416227164..1497314456...4845252741

..636698..6763143..46732687..247920339.1090826214..4179700035..14425457557

.1151966.13496424.100636591..570069808.2669230399.10893560939..40183952539

.2005704.25706057.205574323.1239033996.6166331968.26828743607.106069534256

Links

R. H. Hardin, Table of n, a(n) for n = 1..1404

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

Formula

Empirical: T(n,k) is a polynomial of degree 2k+7 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..1..1....0..0..0..1....0..0..0..2....0..0..0..1
..0..0..0..2....1..1..1..2....0..0..0..1....1..1..1..2....0..0..1..2
..0..0..1..2....1..1..1..2....0..0..0..1....1..1..1..2....0..1..2..2
..0..1..1..2....1..1..2..1....1..1..2..1....1..1..1..2....0..2..0..0
..2..1..1..2....1..2..0..2....2..2..1..0....1..1..2..2....0..2..2..2

Crossrefs

Sequence in context: A227485 A252009 A032744 * A185469 A065656 A185468

Adjacent sequences: A185474 A185475 A185476 * A185478 A185479 A185480

Keyword

nonn,tabl

Author

R. H. Hardin, General degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Jan 28 2011

Status

approved