A204263 Symmetric matrix: f(i,j)=(i+j mod 3), by antidiagonals.

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

Offset: 1

Author

Clark Kimberling, Jan 15 2012

Keywords

• nonn
• tabl

Comments

A block matrix over {0,1,2}. In the following guide to related matrices and permanents, Duvwxyz represents the matrix remaining after row 1 of the matrix Auvwxyz is deleted:

Matrix................Permanent of n-th submatrix

A204263=D204421.......A204265

A204267=D204263.......A204268

A204421=D204267.......A179079

A204423=D204425.......A204424

A204425=D204427.......A204426

A204427=D204423.......A204428

A204429=D204431.......A204430

A204431=D204433.......A204432

A204433=D204429.......A204434

Examples

			Northwest corner:
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
1 2 0 1 2 0
		

Links

• G. C. Greubel, Table of n, a(n) for the first 100 antidiagonals, flattened

Crossrefs

Cf. A204265.

Programs

Mathematica

f[i_, j_] := Mod[i + j, 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}]]      (* A204263 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 22}]    (* A204265 *)