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Symmetric matrix based by antidiagonals, based on f(i,j)=min{1+(j mod i), 1+( i mod j)}.
3

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

%S 1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,2,2,2,2,1,1,1,3,1,3,1,1,1,2,1,2,2,1,

%T 2,1,1,1,2,3,1,3,2,1,1,1,2,3,4,2,2,4,3,2,1,1,1,1,1,3,1,3,1,1,1,1,1,2,

%U 2,2,4,2,2,4,2,2,2,1,1,1,3,3,5,3,1,3,5,3,3,1,1,1,2,1,4,1,4,2,2

%N Symmetric matrix based by antidiagonals, based on f(i,j)=min{1+(j mod i), 1+( i mod j)}.

%C A204014 represents the matrix M given by f(i,j)=min{1+(j mod i), 1+( i mod j)} for i>=1 and j>=1. See A204015 for characteristic polynomials of principal submatrices of M, with interlacing zeros.

%e Northwest corner:

%e 1 1 1 1 1 1

%e 1 1 2 1 2 1

%e 1 2 1 2 3 1

%e 1 1 2 1 2 3

%e 1 2 3 2 1 2

%t f[i_, j_] := Min[1 + Mod[i, j], 1 + Mod[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}]] (* A204014 *)

%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[%] (* A204015 *)

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

%Y Cf. A204015, A202453.

%K nonn,tabl

%O 1,8

%A _Clark Kimberling_, Jan 10 2012