A204012 Symmetric matrix based on f(i,j)=min{3i+j-3,i+3j-3}, by antidiagonals.

1, 2, 2, 3, 5, 3, 4, 6, 6, 4, 5, 7, 9, 7, 5, 6, 8, 10, 10, 8, 6, 7, 9, 11, 13, 11, 9, 7, 8, 10, 12, 14, 14, 12, 10, 8, 9, 11, 13, 15, 17, 15, 13, 11, 9, 10, 12, 14, 16, 18, 18, 16, 14, 12, 10, 11, 13, 15, 17, 19, 21, 19, 17, 15, 13, 11, 12, 14, 16, 18, 20, 22, 22, 20, 18

Offset: 1

Author

Clark Kimberling, Jan 10 2012

Keywords

• nonn
• tabl

Comments

A204012 represents the matrix M given by f(i,j)=max{3i+j-3,i+3j-3}for i>=1 and j>=1. See A204013 for characteristic polynomials of principal submatrices of M, with interlacing zeros.

Examples

			Northwest corner:
1....2....3....4....5....6
2....5....6....7....8....9
3....6....9....10...11...12
4....7....10...13...14...15
		

Crossrefs

Cf. A204013, A202453.

Programs

Mathematica

f[i_, j_] := Min[3 i + j - 3, 3 j + i - 3];
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}]]   (* A204012 *)
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[%]  (* A204013 *)
TableForm[Table[c[n], {n, 1, 10}]]