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A204014
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Symmetric matrix based by antidiagonals, based on f(i,j)=min{1+(j mod i), 1+( i mod j)}.
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3
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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, 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, 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
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OFFSET
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1,8
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COMMENTS
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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.
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LINKS
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EXAMPLE
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Northwest corner:
1 1 1 1 1 1
1 1 2 1 2 1
1 2 1 2 3 1
1 1 2 1 2 3
1 2 3 2 1 2
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MATHEMATICA
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f[i_, j_] := Min[1 + Mod[i, j], 1 + Mod[j, i]];
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[6]] (* 6x6 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
{n, 1, 12}, {i, 1, n}]] (* A204014 *)
p[n_] := CharacteristicPolynomial[m[n], x];
c[n_] := CoefficientList[p[n], x]
TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
Table[c[n], {n, 1, 12}]
TableForm[Table[c[n], {n, 1, 10}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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