https://oeis.org/A085000 For an nbyn matrix one could substitute in the determinant that gives the maximum result n<--n+1, n+1<--n+2 and so on to give a number of different increasing results that could be used to find the polynomial expressing these terms. Would this polynomial always be what would produce the maximum result for the determinant of the matrix being examined? Thus for a 3by3 the simple polynomial is 332+$80*n$ gives 412 for n=1..9, 492 n=2..10, 572 for n=3..11 and so on. Would this logic be valid for all larger matrices and their maximum determinants?
2026-04-29 20:23:08.1777494188
polynomial for maximums in A085000
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For any finite sequence $a_1,\ldots,a_n$ you can find a polynomial $P$ such that $$\forall i\in\{1,\ldots, n\},\ \ P(i)=a_i.$$
There is however no reason to believe that this polynomial will still give out whatever expected values when $i>n$. To do this you would need to consider another polynomial, most likely of a higher degree. As the degree increases, to cover an infinite sequence you would need a "polynomial of infinite degree", which is something that does exist but is not called a polynomial.