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%I #5 Mar 30 2012 18:58:07
%S 2,3,3,4,6,4,5,8,8,5,6,10,12,10,6,7,12,15,15,12,7,8,14,18,20,18,14,8,
%T 9,16,21,24,24,21,16,9,10,18,24,28,30,28,24,18,10,11,20,27,32,35,35,
%U 32,27,20,11,12,22,30,36,40,42,40,36,30,22,12,13,24,33,40,45,48
%N Symmetric matrix based on f(i,j)=min{i(j+1),j(i+1)}, by antidiagonals.
%C A203996 represents the matrix M given by f(i,j)=min{i(j+1),j(i+1)} for i>=1 and j>=1. See A203997 for characteristic polynomials of principal submatrices of M, with interlacing zeros.
%e Northwest corner:
%e 2...3....4....5....6....7
%e 3...6....8....10...12...14
%e 4...8....12...15...18...21
%e 5...10...15...20...24...28
%t f[i_, j_] := Min[i (j + 1), j (i + 1)];
%t m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t TableForm[m[6]] (* 6x6 principal submatrix *)
%t Flatten[Table[f[i, n + 1 - i],
%t {n, 1, 12}, {i, 1, n}]] (* A203996 *)
%t p[n_] := CharacteristicPolynomial[m[n], x];
%t c[n_] := CoefficientList[p[n], x]
%t TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t Table[c[n], {n, 1, 12}]
%t Flatten[%] (* A203997 *)
%t TableForm[Table[c[n], {n, 1, 10}]]
%Y Cf. A203995, A202453.
%K nonn,tabl
%O 1,1
%A _Clark Kimberling_, Jan 09 2012
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