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%I #8 Dec 09 2018 12:09:17
%S 2066505,59969593,59969593,1276581035,2974946682,1276581035,
%T 22000126445,99241308567,99241308567,22000126445,319741716426,
%U 2536761070723,4813465754996,2536761070723,319741716426,4028133387613,52666517720011
%N 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
%C Table starts
%C ...........2066505.............59969593.............1276581035
%C ..........59969593...........2974946682............99241308567
%C ........1276581035..........99241308567..........4813465754996
%C .......22000126445........2536761070723........171334955820947
%C ......319741716426.......52666517720011.......4805827783188400
%C .....4028133387613......921058887545363.....110909004238159456
%C ....44902749582723....13921822487031205....2169936652932512523
%C ...449959668016830...185414592506642580...36804096662464163093
%C ..4103914508092780..2208956268019713255..550615265988952206164
%C .34409633745323847.23828517723857362267.7367827886026471340866
%H R. H. Hardin, <a href="/A186915/b186915.txt">Table of n, a(n) for n = 1..126</a>
%H R. H. Hardin, <a href="/A186915/a186915.txt">Polynomials for columns 1-5</a>
%F Empirical: T(n,k) is a polynomial of degree 6k+77, for fixed k.
%F 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.
%F Then empirically T(n,k,z) is a polynomial of degree z*k + z*(z+1)*(z+5)/6 in n, for fixed k.
%e Some solutions for 5X4
%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e ..1..1..3..3....1..1..1..5....0..1..4..6....0..1..5..6....1..2..4..4
%e ..1..4..5..5....5..5..5..6....0..3..2..5....1..5..6..0....5..6..0..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, general degree formula intuited by _D. S. McNeil_ in the Sequence Fans Mailing List, Feb 28 2011
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