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A204000 Symmetric matrix based on f(i,j)=min{i(j+1)-1,j(i+1)-1}, by antidiagonals.

%I A204000 #5 Mar 30 2012 18:58:07
%S A204000 1,2,2,3,5,3,4,7,7,4,5,9,11,9,5,6,11,14,14,11,6,7,13,17,19,17,13,7,8,
%T A204000 15,20,23,23,20,15,8,9,17,23,27,29,27,23,17,9,10,19,26,31,34,34,31,26,
%U A204000 19,10,11,21,29,35,39,41,39,35,29,21,11,12,23,32,39,44,47,47
%N A204000 Symmetric matrix based on f(i,j)=min{i(j+1)-1,j(i+1)-1}, by antidiagonals.
%C A204000 A204000 represents the matrix M given by f(i,j)=min{i(j+1)-1,j(i+1)-1}for i>=1 and j>=1.  See A204001 for characteristic polynomials of principal submatrices of M, with interlacing zeros.
%e A204000 Northwest corner:
%e A204000 1...2....3....4....5....6
%e A204000 2...5....7....9....11...13
%e A204000 3...7....11...14...17...20
%e A204000 4...9....14...19...23...27
%e A204000 5...11...17...23...29...34
%t A204000 f[i_, j_] := Min[i (j + 1) - 1, j (i + 1) - 1];
%t A204000 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204000 TableForm[m[6]] (* 6x6 principal submatrix *)
%t A204000 Flatten[Table[f[i, n + 1 - i],
%t A204000 {n, 1, 12}, {i, 1, n}]]    (* A204000 *)
%t A204000 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204000 c[n_] := CoefficientList[p[n], x]
%t A204000 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204000 Table[c[n], {n, 1, 12}]
%t A204000 Flatten[%]              (* A204001 *)
%t A204000 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204000 Cf. A204001, A202453.
%K A204000 nonn,tabl
%O A204000 1,2
%A A204000 _Clark Kimberling_, Jan 09 2012