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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
10
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
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
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