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A186915 T(n,k)=Number of (n+2)X(k+2) 0..6 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order 10
2066505, 59969593, 59969593, 1276581035, 2974946682, 1276581035, 22000126445, 99241308567, 99241308567, 22000126445, 319741716426, 2536761070723, 4813465754996, 2536761070723, 319741716426, 4028133387613, 52666517720011 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

...........2066505.............59969593.............1276581035

..........59969593...........2974946682............99241308567

........1276581035..........99241308567..........4813465754996

.......22000126445........2536761070723........171334955820947

......319741716426.......52666517720011.......4805827783188400

.....4028133387613......921058887545363.....110909004238159456

....44902749582723....13921822487031205....2169936652932512523

...449959668016830...185414592506642580...36804096662464163093

..4103914508092780..2208956268019713255..550615265988952206164

.34409633745323847.23828517723857362267.7367827886026471340866

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..126

R. H. Hardin, Polynomials for columns 1-5

FORMULA

Empirical: T(n,k) is a polynomial of degree 6k+77, 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..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0

..1..1..3..3....1..1..1..5....0..1..4..6....0..1..5..6....1..2..4..4

..1..4..5..5....5..5..5..6....0..3..2..5....1..5..6..0....5..6..0..1

CROSSREFS

Sequence in context: A206667 A251512 A113568 * A186907 A186906 A155125

Adjacent sequences:  A186912 A186913 A186914 * A186916 A186917 A186918

KEYWORD

nonn,tabl

AUTHOR

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

STATUS

approved

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Last modified January 22 04:27 EST 2020. Contains 331133 sequences. (Running on oeis4.)