A204014 Symmetric matrix based by antidiagonals, based on f(i,j)=min{1+(j mod i), 1+( i mod j)}.

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

Offset: 1

Author

Clark Kimberling, Jan 10 2012

Keywords

• nonn
• tabl

Comments

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.

Examples

			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
		

Crossrefs

Cf. A204015, A202453.

Programs

Mathematica

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}]
Flatten[%]               (* A204015 *)
TableForm[Table[c[n], {n, 1, 10}]]