A203996 Symmetric matrix based on f(i,j)=min{i(j+1),j(i+1)}, by antidiagonals.

2, 3, 3, 4, 6, 4, 5, 8, 8, 5, 6, 10, 12, 10, 6, 7, 12, 15, 15, 12, 7, 8, 14, 18, 20, 18, 14, 8, 9, 16, 21, 24, 24, 21, 16, 9, 10, 18, 24, 28, 30, 28, 24, 18, 10, 11, 20, 27, 32, 35, 35, 32, 27, 20, 11, 12, 22, 30, 36, 40, 42, 40, 36, 30, 22, 12, 13, 24, 33, 40, 45, 48

Offset: 1

Author

Clark Kimberling, Jan 09 2012

Keywords

• nonn
• tabl

Comments

A203996 represents the matrix M given by f(i,j)=min{i(j+1),j(i+1)} for i>=1 and j>=1. See A203997 for characteristic polynomials of principal submatrices of M, with interlacing zeros.

Examples

			Northwest corner:
2...3....4....5....6....7
3...6....8....10...12...14
4...8....12...15...18...21
5...10...15...20...24...28
		

Crossrefs

Cf. A203995, A202453.

Programs

Mathematica

f[i_, j_] := Min[i (j + 1), j (i + 1)];
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}]]   (* A203996 *)
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[%]      (* A203997 *)
TableForm[Table[c[n], {n, 1, 10}]]