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Symmetric matrix based on f(i,j)=min{2i+j,i+2j}, by antidiagonals.
3

%I #5 Mar 30 2012 18:58:07

%S 3,4,4,5,6,5,6,7,7,6,7,8,9,8,7,8,9,10,10,9,8,9,10,11,12,11,10,9,10,11,

%T 12,13,13,12,11,10,11,12,13,14,15,14,13,12,11,12,13,14,15,16,16,15,14,

%U 13,12,13,14,15,16,17,18,17,16,15,14,13,14,15,16,17,18,19,19

%N Symmetric matrix based on f(i,j)=min{2i+j,i+2j}, by antidiagonals.

%C A204002 represents the matrix M given by f(i,j)=min{2i+j,i+2j}for i>=1 and j>=1. See A204003 for characteristic polynomials of principal submatrices of M, with interlacing zeros.

%e Northwest corner:

%e 3...4...5....6....7....8

%e 4...6...7....8....9....10

%e 5...7...9....10...11...12

%e 6...8...10...12...13...14

%t f[i_, j_] := Min[2 i + j, 2 j + i];

%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}]] (* A204002 *)

%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[%] (* A204003 *)

%t TableForm[Table[c[n], {n, 1, 10}]]

%Y Cf. A204003, A202453.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Jan 09 2012