A204156 Symmetric matrix based on f(i,j)=max(3i-j, 3j-i), by antidiagonals.

1, 4, 4, 7, 3, 7, 10, 6, 6, 10, 13, 9, 5, 9, 13, 16, 12, 8, 8, 12, 16, 19, 15, 11, 7, 11, 15, 19, 22, 18, 14, 10, 10, 14, 18, 22, 25, 21, 17, 13, 9, 13, 17, 21, 25, 28, 24, 20, 16, 12, 12, 16, 20, 24, 28, 31, 27, 23, 19, 15, 11, 15, 19, 23, 27, 31, 34, 30, 26, 22, 18

Offset: 1

Author

Clark Kimberling, Jan 12 2012

Keywords

• nonn
• tabl

Comments

A204156 represents the matrix M given by f(i,j)=max(3i-j, 3j-i) for i>=1 and j>=1. See A204157 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...4...7...10..13
4...3...6...9...12
7...6...5...8...11
10..9...8...7...10
		

Crossrefs

Cf. A204157, A204016, A202453.

Programs

Mathematica

f[i_, j_] := -1 + Max[3 i - j, 3 j - i];
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
  {n, 1, 15}, {i, 1, n}]]    (* A204156 *)
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[%]                   (* A204157 *)
TableForm[Table[c[n], {n, 1, 10}]]