A204000 Symmetric matrix based on f(i,j)=min{i(j+1)-1,j(i+1)-1}, by antidiagonals.

1, 2, 2, 3, 5, 3, 4, 7, 7, 4, 5, 9, 11, 9, 5, 6, 11, 14, 14, 11, 6, 7, 13, 17, 19, 17, 13, 7, 8, 15, 20, 23, 23, 20, 15, 8, 9, 17, 23, 27, 29, 27, 23, 17, 9, 10, 19, 26, 31, 34, 34, 31, 26, 19, 10, 11, 21, 29, 35, 39, 41, 39, 35, 29, 21, 11, 12, 23, 32, 39, 44, 47, 47

Offset: 1

Author

Clark Kimberling, Jan 09 2012

Keywords

• nonn
• tabl

Comments

A204000 represents the matrix M given by f(i,j)=min{i(j+1)-1,j(i+1)-1}for i>=1 and j>=1. See A204001 for characteristic polynomials of principal submatrices of M, with interlacing zeros.

Examples

			Northwest corner:
1...2....3....4....5....6
2...5....7....9....11...13
3...7....11...14...17...20
4...9....14...19...23...27
5...11...17...23...29...34
		

Crossrefs

Cf. A204001, A202453.

Programs

Mathematica

f[i_, j_] := Min[i (j + 1) - 1, j (i + 1) - 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}]]    (* A204000 *)
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[%]              (* A204001 *)
TableForm[Table[c[n], {n, 1, 10}]]