A204006 Symmetric matrix based on f(i,j) = min{2i+j-2,i+2j-2}, by antidiagonals.

1, 2, 2, 3, 4, 3, 4, 5, 5, 4, 5, 6, 7, 6, 5, 6, 7, 8, 8, 7, 6, 7, 8, 9, 10, 9, 8, 7, 8, 9, 10, 11, 11, 10, 9, 8, 9, 10, 11, 12, 13, 12, 11, 10, 9, 10, 11, 12, 13, 14, 14, 13, 12, 11, 10, 11, 12, 13, 14, 15, 16, 15, 14, 13, 12, 11, 12, 13, 14, 15, 16, 17, 17, 16, 15, 14, 13, 12

Offset: 1

Author

Clark Kimberling, Jan 09 2012

Keywords

• nonn
• tabl

Comments

A204006 represents the matrix M given by f(i,j) = min{2i+j,i+2j} for i>=1 and j>=1. See A204007 for characteristic polynomials of principal submatrices of M, with interlacing zeros.

Examples

			Northwest corner:
1...2...3...4....5....6
2...4...5...6....7....8
3...5...7...8....9....10
4...6...8...10...11...12
		

Crossrefs

Cf. A204007, A202453.

Programs

Mathematica

f[i_, j_] := Min[2 i + j - 2, 2 j + i - 2];
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}]]   (* A204006 *)
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[%]                (* A204007 *)
TableForm[Table[c[n], {n, 1, 10}]]