A204028 Symmetric matrix based on f(i,j)=min(3i-2,3j-2), by antidiagonals.

1, 1, 1, 1, 4, 1, 1, 4, 4, 1, 1, 4, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 10, 7, 4, 1, 1, 4, 7, 10, 10, 7, 4, 1, 1, 4, 7, 10, 13, 10, 7, 4, 1, 1, 4, 7, 10, 13, 13, 10, 7, 4, 1, 1, 4, 7, 10, 13, 16, 13, 10, 7, 4, 1, 1, 4, 7, 10, 13, 16, 16, 13, 10, 7, 4, 1, 1, 4, 7, 10, 13, 16, 19, 16

Offset: 1

Author

Clark Kimberling, Jan 11 2012

Keywords

• nonn
• tabl

Comments

A204028 represents the matrix M given by f(i,j)=min(3i-2,3j-2) for i>=1 and j>=1. See A204029 for characteristic polynomials of principal submatrices of M, with interlacing zeros. See A204016 for a guide to other choices of M.

Examples

			Northwest corner:
1...1...1...1....1....1
1...4...4...4....4....4
1...4...7...7....7....7
1...4...7...10...10...10
1...4...7...10...13...13
		

Crossrefs

Cf. A204029, A204016, A202453.

Programs

Mathematica

f[i_, j_] := Min[3 i - 2, 3 j - 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, 15}, {i, 1, n}]]  (* A204028 *)
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[%]                 (* A204029 *)
TableForm[Table[c[n], {n, 1, 10}]]