A204002 Symmetric matrix based on f(i,j)=min{2i+j,i+2j}, by antidiagonals.

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, 12, 13, 13, 12, 11, 10, 11, 12, 13, 14, 15, 14, 13, 12, 11, 12, 13, 14, 15, 16, 16, 15, 14, 13, 12, 13, 14, 15, 16, 17, 18, 17, 16, 15, 14, 13, 14, 15, 16, 17, 18, 19, 19

Offset: 1

Author

Clark Kimberling, Jan 09 2012

Keywords

• nonn
• tabl

Comments

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.

Examples

			Northwest corner:
3...4...5....6....7....8
4...6...7....8....9....10
5...7...9....10...11...12
6...8...10...12...13...14
		

Crossrefs

Cf. A204003, A202453.

Programs

Mathematica

f[i_, j_] := Min[2 i + j, 2 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}]]    (* A204002 *)
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[%]                 (* A204003 *)
TableForm[Table[c[n], {n, 1, 10}]]