A204158 Symmetric matrix based on f(i,j)=max(3i-2j, 3j-2i), by antidiagonals.

1, 4, 4, 7, 2, 7, 10, 5, 5, 10, 13, 8, 3, 8, 13, 16, 11, 6, 6, 11, 16, 19, 14, 9, 4, 9, 14, 19, 22, 17, 12, 7, 7, 12, 17, 22, 25, 20, 15, 10, 5, 10, 15, 20, 25, 28, 23, 18, 13, 8, 8, 13, 18, 23, 28, 31, 26, 21, 16, 11, 6, 11, 16, 21, 26, 31, 34, 29, 24, 19, 14, 9, 9, 14

Offset: 1

Author

Clark Kimberling, Jan 12 2012

Keywords

• nonn
• tabl

Comments

A204158 represents the matrix M given by f(i,j)=max(3i-2j, 3j-2i) for i>=1 and j>=1. See A204159 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....2....5....8....11
7....5....3....6....9
10...8....6....4....7
		

Crossrefs

Cf. A204159, A204016, A202453.

Programs

Mathematica

f[i_, j_] := Max[3 i - 2 j, 3 j - 2 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}]]   (* A204158 *)
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[%]                  (* A204159 *)
TableForm[Table[c[n], {n, 1, 10}]]