[seqfan] Arrays with interior sorting, guess the series

[Ron Hardin]

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,1) is a polynomial of degree 1*k+2 in n, for fixed k
T(n,k,2) is a polynomial of degree 2*k+8 in n, for fixed k
T(n,k,3) is a polynomial of degree 3*k+16 in n, for fixed k
T(n,k,4) is a polynomial of degree 4*k+30 in n, for fixed k
T(n,k,5) is a polynomial of degree 5*k+50 in n, for fixed k
T(n,k,6) is a polynomial of degree 6*k+77 in n, for fixed k
T(n,k,7) is a polynomial of degree 7*k+112 in n, for fixed k

what's 2,8,16,30,50,77,112 ?


 rhhardin at mindspring.com
rhhardin at att.net (either)