A204421 Symmetric matrix: f(i,j)=(i+j+2 mod 3), by antidiagonals.

1, 2, 2, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Author

Clark Kimberling, Jan 15 2012

Keywords

• nonn
• tabl

Comments

A block matrix over {0,1,2}. See A204263 for a guide to related matrices and permanents.

Examples

			Northwest corner:
1 2 0 1 2 0
2 0 1 2 0 1
0 1 2 0 1 2
1 2 0 1 2 0
2 0 1 2 0 1
0 1 2 0 1 2
		

Crossrefs

Cf. A179079, A204263.

Programs

Mathematica

f[i_, j_] := Mod[i + j + 2, 3];
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, 14}, {i, 1, n}]]    (* A204421 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 22}]  (* A179079 *)