A204175 Symmetric matrix based on f(i,j)=(1 if max(i,j) is even, and 0 otherwise), by antidiagonals.

0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1

Offset

1

Comments

A204175 represents the matrix M given by f(i,j)=(1 if max(i,j) is even, and 0 otherwise) for i>=1 and j>=1. See A204176 for characteristic polynomials of principal submatrices of M, with interlacing zeros. See A204016 for a guide to other choices of M.

Links

Table of n, a(n) for n=1..99.

Example

Northwest corner:
0 1 0 1 0 1 0 1
1 1 0 1 0 1 0 1
0 0 0 1 0 1 0 1
1 1 1 1 0 1 0 1
0 0 0 0 0 1 0 1
1 1 1 1 1 1 0 1

Mathematica

f[i_, j_] := If[Mod[Max[i, j], 2] == 0, 1, 0]
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}]]  (* A204175 *)
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[%]                 (* A204176 *)
TableForm[Table[c[n], {n, 1, 10}]]

Crossrefs

Cf. A204176, A204016, A202453.

Sequence in context: A131929 A100821 A139689 * A343173 A285255 A324823

Adjacent sequences: A204172 A204173 A204174 * A204176 A204177 A204178

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 12 2012

Status

approved